diff --git a/sklearn/linear_model/ransac.py b/sklearn/linear_model/ransac.py
index 12c45b26aa567..db60ddb90b378 100644
--- a/sklearn/linear_model/ransac.py
+++ b/sklearn/linear_model/ransac.py
@@ -11,7 +11,7 @@
 from ..utils.random import sample_without_replacement
 from ..utils.validation import check_is_fitted
 from .base import LinearRegression
-
+from ..utils.validation import has_fit_parameter
 
 _EPSILON = np.spacing(1)
 
@@ -177,7 +177,7 @@ def __init__(self, base_estimator=None, min_samples=None,
         self.residual_metric = residual_metric
         self.random_state = random_state
 
-    def fit(self, X, y):
+    def fit(self, X, y, sample_weight=None):
         """Fit estimator using RANSAC algorithm.
 
         Parameters
@@ -188,6 +188,11 @@ def fit(self, X, y):
         y : array-like, shape = [n_samples] or [n_samples, n_targets]
             Target values.
 
+        sample_weight: array-like, shape = [n_samples]
+            Individual weights for each sample
+            raises error if sample_weight is passed and base_estimator
+            fit method does not support it.
+
         Raises
         ------
         ValueError
@@ -243,6 +248,17 @@ def fit(self, X, y):
         except ValueError:
             pass
 
+        estimator_fit_has_sample_weight = has_fit_parameter(base_estimator,
+                                                            "sample_weight")
+        estimator_name = type(base_estimator).__name__
+        if (sample_weight is not None and not
+                estimator_fit_has_sample_weight):
+            raise ValueError("%s does not support sample_weight. Samples"
+                             " weights are only used for the calibration"
+                             " itself." % estimator_name)
+        if sample_weight is not None:
+            sample_weight = np.asarray(sample_weight)
+
         n_inliers_best = 0
         score_best = np.inf
         inlier_mask_best = None
@@ -269,7 +285,11 @@ def fit(self, X, y):
                 continue
 
             # fit model for current random sample set
-            base_estimator.fit(X_subset, y_subset)
+            if sample_weight is None:
+                base_estimator.fit(X_subset, y_subset)
+            else:
+                base_estimator.fit(X_subset, y_subset,
+                                   sample_weight=sample_weight[subset_idxs])
 
             # check if estimated model is valid
             if (self.is_model_valid is not None and not
diff --git a/sklearn/linear_model/tests/test_ransac.py b/sklearn/linear_model/tests/test_ransac.py
index b646653acbe76..1a5f73c666292 100644
--- a/sklearn/linear_model/tests/test_ransac.py
+++ b/sklearn/linear_model/tests/test_ransac.py
@@ -1,11 +1,9 @@
 import numpy as np
-from numpy.testing import assert_equal, assert_raises
-from numpy.testing import assert_array_almost_equal
-from sklearn.utils.testing import assert_raises_regexp
+from numpy.testing import assert_equal, assert_raises, assert_array_equal,assert_array_almost_equal
+from sklearn.utils.testing import assert_raises_regexp, assert_almost_equal, assert_less
 from scipy import sparse
-
-from sklearn.utils.testing import assert_less
-from sklearn.linear_model import LinearRegression, RANSACRegressor
+from sklearn.utils import check_random_state
+from sklearn.linear_model import LinearRegression, RANSACRegressor,Lasso
 from sklearn.linear_model.ransac import _dynamic_max_trials
 
 
@@ -353,3 +351,49 @@ def test_ransac_dynamic_max_trials():
     ransac_estimator = RANSACRegressor(base_estimator, min_samples=2,
                                        stop_probability=1.1)
     assert_raises(ValueError, ransac_estimator.fit, X, y)
+
+
+def test_ransac_fit_sample_weight():
+    ransac_estimator = RANSACRegressor(random_state=0)
+    n_samples = y.shape[0]
+    weights = np.ones(n_samples)
+    ransac_estimator.fit(X, y, weights)
+    # sanity check
+    assert_equal(ransac_estimator.inlier_mask_.shape[0], n_samples)
+
+    ref_inlier_mask = np.ones_like(ransac_estimator.inlier_mask_
+                                   ).astype(np.bool_)
+    ref_inlier_mask[outliers] = False
+    # check that mask is correct
+    assert_array_equal(ransac_estimator.inlier_mask_, ref_inlier_mask)
+
+    # check that fit(X)  = fit([X1, X2, X3],sample_weight = [n1, n2, n3]) where
+    #   X = X1 repeated n1 times, X2 repeated n2 times and so forth
+    random_state = check_random_state(0)
+    X_ = random_state.randint(0, 200, [10, 1])
+    y_ = np.ndarray.flatten(0.2 * X_ + 2)
+    sample_weight = random_state.randint(0, 10, 10)
+    outlier_X = random_state.randint(0, 1000, [1, 1])
+    outlier_weight = random_state.randint(0, 10, 1)
+    outlier_y = random_state.randint(-1000, 0, 1)
+
+    X_flat = np.append(np.repeat(X_, sample_weight, axis=0),
+                       np.repeat(outlier_X, outlier_weight, axis=0), axis=0)
+    y_flat = np.ndarray.flatten(np.append(np.repeat(y_, sample_weight, axis=0),
+                                np.repeat(outlier_y, outlier_weight, axis=0),
+                                          axis=0))
+    ransac_estimator.fit(X_flat, y_flat)
+    ref_coef_ = ransac_estimator.estimator_.coef_
+
+    sample_weight = np.append(sample_weight, outlier_weight)
+    X_ = np.append(X_, outlier_X, axis=0)
+    y_ = np.append(y_, outlier_y)
+    ransac_estimator.fit(X_, y_, sample_weight)
+
+    assert_almost_equal(ransac_estimator.estimator_.coef_, ref_coef_)
+
+    # check that if base_estimator.fit doesn't support
+    # sample_weight, raises error
+    base_estimator = Lasso()
+    ransac_estimator = RANSACRegressor(base_estimator)
+    assert_raises(ValueError, ransac_estimator.fit, X, y, weights)