diff --git a/gtsam/linear/SparseEigenSolver.cpp b/gtsam/linear/SparseEigenSolver.cpp
new file mode 100644
index 000000000..f0dfd83f3
--- /dev/null
+++ b/gtsam/linear/SparseEigenSolver.cpp
@@ -0,0 +1,231 @@
+/* ----------------------------------------------------------------------------
+
+ * GTSAM Copyright 2010, Georgia Tech Research Corporation,
+ * Atlanta, Georgia 30332-0415
+ * All Rights Reserved
+ * Authors: Frank Dellaert, et al. (see THANKS for the full author list)
+
+ * See LICENSE for the license information
+
+ * -------------------------------------------------------------------------- */
+
+/**
+ * @file SparseEigenSolver.cpp
+ *
+ * @brief Eigen SparseSolver based linear solver backend for GTSAM
+ *
+ * @date Aug 2019
+ * @author Mandy Xie
+ * @author Fan Jiang
+ * @author Frank Dellaert
+ */
+
+#include <gtsam/base/timing.h>
+#include <gtsam/linear/SparseEigenSolver.h>
+#include <vector>
+
+#include <boost/shared_ptr.hpp>
+
+using namespace std;
+
+namespace gtsam {
+
+  using SpMat = Eigen::SparseMatrix<double, Eigen::ColMajor, Eigen::Index>;
+
+  Eigen::SparseMatrix<double>
+  SparseEigenSolver::sparseJacobianEigen(
+      const GaussianFactorGraph &gfg,
+      const Ordering &ordering) {
+    // First find dimensions of each variable
+    std::map<Key, size_t> dims;
+    for (const boost::shared_ptr<GaussianFactor> &factor : gfg) {
+      if (!static_cast<bool>(factor))
+        continue;
+
+      for (auto it = factor->begin(); it != factor->end(); ++it) {
+        dims[*it] = factor->getDim(it);
+      }
+    }
+
+    // Compute first scalar column of each variable
+    size_t currentColIndex = 0;
+    std::map<Key, size_t> columnIndices;
+    for (const auto key : ordering) {
+      columnIndices[key] = currentColIndex;
+      currentColIndex += dims[key];
+    }
+
+    // Iterate over all factors, adding sparse scalar entries
+    vector<Eigen::Triplet<double>> entries;
+    entries.reserve(60 * gfg.size());
+
+    size_t row = 0;
+    for (const boost::shared_ptr<GaussianFactor> &factor : gfg) {
+      if (!static_cast<bool>(factor)) continue;
+
+      // Convert to JacobianFactor if necessary
+      JacobianFactor::shared_ptr jacobianFactor(
+          boost::dynamic_pointer_cast<JacobianFactor>(factor));
+      if (!jacobianFactor) {
+        HessianFactor::shared_ptr hessian(
+            boost::dynamic_pointer_cast<HessianFactor>(factor));
+        if (hessian)
+          jacobianFactor.reset(new JacobianFactor(*hessian));
+        else
+          throw invalid_argument(
+              "GaussianFactorGraph contains a factor that is neither a JacobianFactor nor a HessianFactor.");
+      }
+
+      // Whiten the factor and add entries for it
+      // iterate over all variables in the factor
+      const JacobianFactor whitened(jacobianFactor->whiten());
+      for (JacobianFactor::const_iterator key = whitened.begin();
+           key < whitened.end(); ++key) {
+        JacobianFactor::constABlock whitenedA = whitened.getA(key);
+        // find first column index for this key
+        size_t column_start = columnIndices[*key];
+        for (size_t i = 0; i < (size_t) whitenedA.rows(); i++)
+          for (size_t j = 0; j < (size_t) whitenedA.cols(); j++) {
+            double s = whitenedA(i, j);
+            if (std::abs(s) > 1e-12)
+              entries.emplace_back(row + i, column_start + j, s);
+          }
+      }
+
+      JacobianFactor::constBVector whitenedb(whitened.getb());
+      size_t bcolumn = currentColIndex;
+      for (size_t i = 0; i < (size_t) whitenedb.size(); i++) {
+        double s = whitenedb(i);
+        if (std::abs(s) > 1e-12)
+          entries.emplace_back(row + i, bcolumn, s);
+      }
+
+      // Increment row index
+      row += jacobianFactor->rows();
+    }
+
+    // ...and make a sparse matrix with it.
+    Eigen::SparseMatrix<double, Eigen::ColMajor> Ab(row + 1, currentColIndex + 1);
+    Ab.setFromTriplets(entries.begin(), entries.end());
+    return Ab;
+  }
+
+
+  /// obtain sparse matrix for eigen sparse solver
+  std::pair<SpMat, Eigen::VectorXd> obtainSparseMatrix(
+      const GaussianFactorGraph &gfg,
+      const Ordering &ordering) {
+
+    gttic_(EigenOptimizer_obtainSparseMatrix);
+
+    // Get sparse entries of Jacobian [A|b] augmented with RHS b.
+    auto entries = gfg.sparseJacobian(ordering);
+
+    gttic_(EigenOptimizer_convertSparse);
+    // Convert boost tuples to Eigen triplets
+    vector<Eigen::Triplet<double>> triplets;
+    triplets.reserve(entries.size());
+    size_t rows = 0, cols = 0;
+    for (const auto &e : entries) {
+      size_t temp_rows = e.get<0>(), temp_cols = e.get<1>();
+      triplets.emplace_back(temp_rows, temp_cols, e.get<2>());
+      rows = std::max(rows, temp_rows);
+      cols = std::max(cols, temp_cols);
+    }
+
+    // ...and make a sparse matrix with it.
+    SpMat Ab(rows + 1, cols + 1);
+    Ab.setFromTriplets(triplets.begin(), triplets.end());
+    Ab.makeCompressed();
+    gttoc_(EigenOptimizer_convertSparse);
+
+    gttoc_(EigenOptimizer_obtainSparseMatrix);
+
+    return make_pair<SpMat, Eigen::VectorXd>(Ab.block(0, 0, rows + 1, cols),
+                                             Ab.col(cols));
+  }
+
+  bool SparseEigenSolver::isIterative() {
+    return false;
+  }
+
+  bool SparseEigenSolver::isSequential() {
+    return false;
+  }
+
+  VectorValues SparseEigenSolver::solve(const GaussianFactorGraph &gfg) {
+    if (solverType == QR) {
+      gttic_(EigenOptimizer_optimizeEigenQR);
+      auto Ab_pair = obtainSparseMatrix(gfg, ordering);
+
+      // Solve A*x = b using sparse QR from Eigen
+      gttic_(EigenOptimizer_optimizeEigenQR_create_solver);
+      Eigen::SparseQR<SpMat, Eigen::NaturalOrdering<Eigen::Index>> solver(Ab_pair.first);
+      gttoc_(EigenOptimizer_optimizeEigenQR_create_solver);
+
+      gttic_(EigenOptimizer_optimizeEigenQR_solve);
+      Eigen::VectorXd x = solver.solve(Ab_pair.second);
+      gttoc_(EigenOptimizer_optimizeEigenQR_solve);
+
+      return VectorValues(x, gfg.getKeyDimMap());
+    } else if (solverType == CHOLESKY) {
+      gttic_(EigenOptimizer_optimizeEigenCholesky);
+      SpMat Ab = sparseJacobianEigen(gfg, ordering);
+      auto rows = Ab.rows(), cols = Ab.cols();
+      auto A = Ab.block(0, 0, rows, cols - 1);
+      auto At = A.transpose();
+      auto b = Ab.col(cols - 1);
+
+      SpMat AtA(A.cols(), A.cols());
+      AtA.selfadjointView<Eigen::Upper>().rankUpdate(At);
+
+      gttic_(EigenOptimizer_optimizeEigenCholesky_create_solver);
+      // Solve A*x = b using sparse Cholesky from Eigen
+      Eigen::SimplicialLDLT<SpMat, Eigen::Upper, Eigen::NaturalOrdering<Eigen::Index>>
+          solver(AtA);
+
+      gttoc_(EigenOptimizer_optimizeEigenCholesky_create_solver);
+
+      gttic_(EigenOptimizer_optimizeEigenCholesky_solve);
+      Eigen::VectorXd x = solver.solve(At * b);
+      gttoc_(EigenOptimizer_optimizeEigenCholesky_solve);
+
+      // NOTE: b is reordered now, so we need to transform back the order.
+      // First find dimensions of each variable
+      std::map<Key, size_t> dims;
+      for (const boost::shared_ptr<GaussianFactor> &factor : gfg) {
+        if (!static_cast<bool>(factor))
+          continue;
+
+        for (auto it = factor->begin(); it != factor->end(); ++it) {
+          dims[*it] = factor->getDim(it);
+        }
+      }
+
+      VectorValues vv;
+
+      std::map<Key, size_t> columnIndices;
+
+      {
+        size_t currentColIndex = 0;
+        for (const auto key : ordering) {
+          columnIndices[key] = currentColIndex;
+          currentColIndex += dims[key];
+        }
+      }
+
+      for (const pair<const Key, unsigned long> keyDim : dims) {
+        vv.insert(keyDim.first, x.segment(columnIndices[keyDim.first], keyDim.second));
+      }
+
+      return vv;
+    }
+
+    throw std::exception();
+  }
+
+  SparseEigenSolver::SparseEigenSolver(SparseEigenSolver::SparseEigenSolverType type, const Ordering &ordering) {
+    solverType = type;
+    this->ordering = ordering;
+  }
+}  // namespace gtsam
\ No newline at end of file
diff --git a/gtsam/linear/SparseEigenSolver.h b/gtsam/linear/SparseEigenSolver.h
new file mode 100644
index 000000000..d71365864
--- /dev/null
+++ b/gtsam/linear/SparseEigenSolver.h
@@ -0,0 +1,62 @@
+/* ----------------------------------------------------------------------------
+
+ * GTSAM Copyright 2010, Georgia Tech Research Corporation,
+ * Atlanta, Georgia 30332-0415
+ * All Rights Reserved
+ * Authors: Frank Dellaert, et al. (see THANKS for the full author list)
+
+ * See LICENSE for the license information
+
+ * -------------------------------------------------------------------------- */
+
+/**
+ * @file SparseEigenSolver.h
+ *
+ * @brief Eigen SparseSolver based linear solver backend for GTSAM
+ *
+ * @date Aug 2019
+ * @author Mandy Xie
+ * @author Fan Jiang
+ * @author Frank Dellaert
+ */
+
+#pragma once
+
+#include <gtsam/linear/GaussianFactorGraph.h>
+#include <gtsam/linear/VectorValues.h>
+#include <gtsam/linear/LinearSolver.h>
+#include <Eigen/Sparse>
+#include <string>
+
+namespace gtsam {
+
+  /**
+   * Eigen SparseSolver based Backend class
+   */
+  class GTSAM_EXPORT SparseEigenSolver : public LinearSolver {
+  public:
+
+    typedef enum {
+      QR,
+      CHOLESKY
+    } SparseEigenSolverType;
+
+
+    explicit SparseEigenSolver(SparseEigenSolver::SparseEigenSolverType type, const Ordering &ordering);
+
+    bool isIterative() override;
+
+    bool isSequential() override;
+
+    VectorValues solve(const GaussianFactorGraph &gfg) override;
+
+    static Eigen::SparseMatrix<double>
+    sparseJacobianEigen(const GaussianFactorGraph &gfg, const Ordering &ordering);
+
+  protected:
+
+    SparseEigenSolverType solverType = QR;
+
+    Ordering ordering;
+  };
+}  // namespace gtsam