diff --git a/sklearn/linear_model/cd_fast.pyx b/sklearn/linear_model/cd_fast.pyx
index a51d1bdbdbc96..f3731e3e7b894 100644
--- a/sklearn/linear_model/cd_fast.pyx
+++ b/sklearn/linear_model/cd_fast.pyx
@@ -15,6 +15,7 @@ cimport cython
 from cpython cimport bool
 from cython cimport floating
 import warnings
+from ..exceptions import ConvergenceWarning
 
 ctypedef np.float64_t DOUBLE
 ctypedef np.uint32_t UINT32_t
@@ -302,6 +303,12 @@ def enet_coordinate_descent(np.ndarray[floating, ndim=1] w,
                 if gap < tol:
                     # return if we reached desired tolerance
                     break
+                else:
+                    with gil:
+                        warnings.warn("Objective did not converge."
+                        " You might want to increase the number of iterations.",
+                        ConvergenceWarning)
+
     return w, gap, tol, n_iter + 1
 
 
@@ -521,6 +528,11 @@ def sparse_enet_coordinate_descent(floating [:] w,
                 if gap < tol:
                     # return if we reached desired tolerance
                     break
+                else:
+                    with gil:
+                        warnings.warn("Objective did not converge."
+                        " You might want to increase the number of iterations.",
+                        ConvergenceWarning)
 
     return w, gap, tol, n_iter + 1
 
@@ -675,6 +687,11 @@ def enet_coordinate_descent_gram(floating[:] w, floating alpha, floating beta,
                 if gap < tol:
                     # return if we reached desired tolerance
                     break
+                else:
+                    with gil:
+                        warnings.warn("Objective did not converge."
+                        " You might want to increase the number of iterations.",
+                        ConvergenceWarning)
 
     return np.asarray(w), gap, tol, n_iter + 1
 
@@ -880,5 +897,10 @@ def enet_coordinate_descent_multi_task(floating[::1, :] W, floating l1_reg,
                 if gap < tol:
                     # return if we reached desired tolerance
                     break
+                else:
+                    with gil:
+                        warnings.warn("Objective did not converge."
+                        " You might want to increase the number of iterations.",
+                        ConvergenceWarning)
 
     return np.asarray(W), gap, tol, n_iter + 1
diff --git a/sklearn/linear_model/tests/test_coordinate_descent.py b/sklearn/linear_model/tests/test_coordinate_descent.py
index 834d685f5b23d..90422ccf731a0 100644
--- a/sklearn/linear_model/tests/test_coordinate_descent.py
+++ b/sklearn/linear_model/tests/test_coordinate_descent.py
@@ -818,3 +818,33 @@ def test_coef_shape_not_zero():
     est_no_intercept = Lasso(fit_intercept=False)
     est_no_intercept.fit(np.c_[np.ones(3)], np.ones(3))
     assert est_no_intercept.coef_.shape == (1,)
+
+
+def test_enet_coordinate_descent():
+    """Test that a warning is issued if model does not converge"""
+    clf = Lasso()
+    n_samples = 15500
+    n_features = 500
+    X = np.ones([n_samples, n_features]) * 1e50
+    y = np.ones([n_samples])
+    assert_warns(ConvergenceWarning, clf.fit, X, y)
+
+
+def test_enet_coordinate_descent_gram():
+    """Test that a warning is issued if model does not converge"""
+    clf = Lasso(precompute=True)
+    n_samples = 15500
+    n_features = 500
+    X = np.ones([n_samples, n_features]) * 1e50
+    y = np.ones([n_samples])
+    assert_warns(ConvergenceWarning, clf.fit, X, y)
+
+def test_enet_coordinate_descent_multi_task():
+    """Test that a warning is issued if model does not converge"""
+    clf = MultiTaskLasso()
+    n_samples = 15500
+    n_features = 500
+    n_classes = 2
+    X = np.ones([n_samples, n_features]) * 1e50
+    y = np.ones([n_samples, n_classes])
+    assert_warns(ConvergenceWarning, clf.fit, X, y)
diff --git a/sklearn/linear_model/tests/test_sparse_coordinate_descent.py b/sklearn/linear_model/tests/test_sparse_coordinate_descent.py
index 6b4c09d9742e0..a3526e8d468c1 100644
--- a/sklearn/linear_model/tests/test_sparse_coordinate_descent.py
+++ b/sklearn/linear_model/tests/test_sparse_coordinate_descent.py
@@ -9,6 +9,8 @@
 
 from sklearn.utils.testing import assert_greater
 from sklearn.utils.testing import ignore_warnings
+from sklearn.utils.testing import assert_warns
+from sklearn.exceptions import ConvergenceWarning
 
 from sklearn.linear_model.coordinate_descent import (Lasso, ElasticNet,
                                                      LassoCV, ElasticNetCV)
@@ -291,3 +293,13 @@ def test_same_multiple_output_sparse_dense():
         predict_sparse = l_sp.predict(sample_sparse)
 
         assert_array_almost_equal(predict_sparse, predict_dense)
+
+
+def test_sparse_enet_coordinate_descent():
+    """Test that a warning is issued if model does not converge"""
+    clf = Lasso()
+    n_samples = 15500
+    n_features = 500
+    X = sp.csc_matrix((n_samples, n_features)) * 1e50
+    y = np.ones([n_samples])
+    assert_warns(ConvergenceWarning, clf.fit, X, y)