diff --git a/sklearn/feature_selection/rfe.py b/sklearn/feature_selection/rfe.py
index bbe0cda392290..66985bf9e253c 100644
--- a/sklearn/feature_selection/rfe.py
+++ b/sklearn/feature_selection/rfe.py
@@ -120,7 +120,7 @@ def __init__(self, estimator, n_features_to_select=None, step=1,
     def _estimator_type(self):
         return self.estimator._estimator_type
 
-    def fit(self, X, y):
+    def fit(self, X, y, **fit_params):
         """Fit the RFE model and then the underlying estimator on the selected
            features.
 
@@ -131,10 +131,13 @@ def fit(self, X, y):
 
         y : array-like, shape = [n_samples]
             The target values.
+
+        **fit_params : kwargs
+            Additional parameter passed to the fit function of the estimator.
         """
-        return self._fit(X, y)
+        return self._fit(X, y, **fit_params)
 
-    def _fit(self, X, y, step_score=None):
+    def _fit(self, X, y, step_score=None, **fit_params):
         X, y = check_X_y(X, y, "csc")
         # Initialization
         n_features = X.shape[1]
@@ -166,7 +169,7 @@ def _fit(self, X, y, step_score=None):
             if self.verbose > 0:
                 print("Fitting estimator with %d features." % np.sum(support_))
 
-            estimator.fit(X[:, features], y)
+            estimator.fit(X[:, features], y, **fit_params)
 
             # Get coefs
             if hasattr(estimator, 'coef_'):
diff --git a/sklearn/feature_selection/tests/test_rfe.py b/sklearn/feature_selection/tests/test_rfe.py
index 1efc0279a9dc7..afa0c9a552cda 100644
--- a/sklearn/feature_selection/tests/test_rfe.py
+++ b/sklearn/feature_selection/tests/test_rfe.py
@@ -2,7 +2,8 @@
 Testing Recursive feature elimination
 """
 import numpy as np
-from numpy.testing import assert_array_almost_equal, assert_array_equal
+from numpy.testing import (assert_array_almost_equal, assert_array_equal,
+                           assert_raises)
 from nose.tools import assert_equal, assert_true
 from scipy import sparse
 
@@ -75,6 +76,44 @@ def test_rfe_features_importance():
     assert_array_equal(rfe.get_support(), rfe_svc.get_support())
 
 
+def test_rfe_sample_weights():
+    iris = load_iris()
+    X = iris.data
+    y = iris.target
+
+    clf = SVC(kernel="linear")
+    rfe = RFE(estimator=clf, n_features_to_select=1)
+
+    sample_weight_test = 2
+    class_test = 2
+
+    # Case 1 - original dataset
+    rfe.fit(X, y)
+    ranking_original = rfe.ranking_.copy()
+
+    # Case 2 - double the weight of one class's samples
+    w = np.ones(y.shape[0])
+    w[y == class_test] = sample_weight_test
+
+    rfe.fit(X, y, sample_weight=w)
+    ranking_weights = rfe.ranking_.copy()
+
+    # Case 3 - duplicate the samples of one class
+    extra_X = np.tile(X[y == class_test], (sample_weight_test - 1, 1))
+    X_duplicate = np.concatenate((X, extra_X), axis=0)
+
+    n_extra = (y == class_test).sum() * (sample_weight_test - 1)
+    extra_Y = np.ones(n_extra, dtype=int) * class_test
+    y_duplicate = np.concatenate((y, extra_Y), axis=0)
+
+    rfe.fit(X_duplicate, y_duplicate)
+    ranking_duplicate = rfe.ranking_.copy()
+
+    assert_raises(AssertionError, assert_array_equal, ranking_original,
+                  ranking_weights)
+    assert_array_equal(ranking_weights, ranking_duplicate)
+
+
 def test_rfe():
     generator = check_random_state(0)
     iris = load_iris()