diff --git a/doc/whats_new/v0.21.rst b/doc/whats_new/v0.21.rst
index 0ad582017840f..2494d0dbbcee2 100644
--- a/doc/whats_new/v0.21.rst
+++ b/doc/whats_new/v0.21.rst
@@ -174,6 +174,11 @@ Support for Python 3.4 and below has been officially dropped.
    parameter value ``copy_X=True`` in ``fit``. 
    :issue:`12972` by :user:`Lucio Fernandez-Arjona <luk-f-a>`
 
+- |Fix| Fixed a bug in :class:`linear_model.LinearRegression` that
+  was not returning the same coeffecients and intercepts with
+  ``fit_intercept=True`` in sparse and dense case.
+  :issue:`13279` by `Alexandre Gramfort`_
+
 :mod:`sklearn.manifold`
 ............................
 
diff --git a/sklearn/linear_model/base.py b/sklearn/linear_model/base.py
index eb474f8386189..e194afa94488b 100644
--- a/sklearn/linear_model/base.py
+++ b/sklearn/linear_model/base.py
@@ -459,21 +459,34 @@ def fit(self, X, y, sample_weight=None):
 
         X, y, X_offset, y_offset, X_scale = self._preprocess_data(
             X, y, fit_intercept=self.fit_intercept, normalize=self.normalize,
-            copy=self.copy_X, sample_weight=sample_weight)
+            copy=self.copy_X, sample_weight=sample_weight,
+            return_mean=True)
 
         if sample_weight is not None:
             # Sample weight can be implemented via a simple rescaling.
             X, y = _rescale_data(X, y, sample_weight)
 
         if sp.issparse(X):
+            X_offset_scale = X_offset / X_scale
+
+            def matvec(b):
+                return X.dot(b) - b.dot(X_offset_scale)
+
+            def rmatvec(b):
+                return X.T.dot(b) - X_offset_scale * np.sum(b)
+
+            X_centered = sparse.linalg.LinearOperator(shape=X.shape,
+                                                      matvec=matvec,
+                                                      rmatvec=rmatvec)
+
             if y.ndim < 2:
-                out = sparse_lsqr(X, y)
+                out = sparse_lsqr(X_centered, y)
                 self.coef_ = out[0]
                 self._residues = out[3]
             else:
                 # sparse_lstsq cannot handle y with shape (M, K)
                 outs = Parallel(n_jobs=n_jobs_)(
-                    delayed(sparse_lsqr)(X, y[:, j].ravel())
+                    delayed(sparse_lsqr)(X_centered, y[:, j].ravel())
                     for j in range(y.shape[1]))
                 self.coef_ = np.vstack([out[0] for out in outs])
                 self._residues = np.vstack([out[3] for out in outs])
diff --git a/sklearn/linear_model/tests/test_base.py b/sklearn/linear_model/tests/test_base.py
index bcabe12ed35f3..6fca044c25d86 100644
--- a/sklearn/linear_model/tests/test_base.py
+++ b/sklearn/linear_model/tests/test_base.py
@@ -13,6 +13,7 @@
 from sklearn.utils.testing import assert_array_almost_equal
 from sklearn.utils.testing import assert_almost_equal
 from sklearn.utils.testing import assert_equal
+from sklearn.utils.testing import assert_allclose
 
 from sklearn.linear_model.base import LinearRegression
 from sklearn.linear_model.base import _preprocess_data
@@ -150,6 +151,26 @@ def test_linear_regression_sparse(random_state=0):
         assert_array_almost_equal(ols.predict(X) - y.ravel(), 0)
 
 
+@pytest.mark.parametrize('normalize', [True, False])
+@pytest.mark.parametrize('fit_intercept', [True, False])
+def test_linear_regression_sparse_equal_dense(normalize, fit_intercept):
+    # Test that linear regression agrees between sparse and dense
+    rng = check_random_state(0)
+    n_samples = 200
+    n_features = 2
+    X = rng.randn(n_samples, n_features)
+    X[X < 0.1] = 0.
+    Xcsr = sparse.csr_matrix(X)
+    y = rng.rand(n_samples)
+    params = dict(normalize=normalize, fit_intercept=fit_intercept)
+    clf_dense = LinearRegression(**params)
+    clf_sparse = LinearRegression(**params)
+    clf_dense.fit(X, y)
+    clf_sparse.fit(Xcsr, y)
+    assert clf_dense.intercept_ == pytest.approx(clf_sparse.intercept_)
+    assert_allclose(clf_dense.coef_, clf_sparse.coef_)
+
+
 def test_linear_regression_multiple_outcome(random_state=0):
     # Test multiple-outcome linear regressions
     X, y = make_regression(random_state=random_state)