diff --git a/sklearn/utils/estimator_checks.py b/sklearn/utils/estimator_checks.py
index c3b066e5e31be..fa8e24c588555 100644
--- a/sklearn/utils/estimator_checks.py
+++ b/sklearn/utils/estimator_checks.py
@@ -76,6 +76,7 @@ def _yield_non_meta_checks(name, estimator):
     yield check_sample_weights_pandas_series
     yield check_sample_weights_list
     yield check_estimators_fit_returns_self
+    yield check_complex_data
 
     # Check that all estimator yield informative messages when
     # trained on empty datasets
@@ -458,6 +459,16 @@ def check_dtype_object(name, estimator_orig):
     assert_raises_regex(TypeError, msg, estimator.fit, X, y)
 
 
+def check_complex_data(name, estimator_orig):
+    # check that estimators raise an exception on providing complex data
+    X = np.random.sample(10) + 1j * np.random.sample(10)
+    X = X.reshape(-1, 1)
+    y = np.random.sample(10) + 1j * np.random.sample(10)
+    estimator = clone(estimator_orig)
+    assert_raises_regex(ValueError, "Complex data not supported",
+                        estimator.fit, X, y)
+
+
 @ignore_warnings
 def check_dict_unchanged(name, estimator_orig):
     # this estimator raises
diff --git a/sklearn/utils/tests/test_validation.py b/sklearn/utils/tests/test_validation.py
index 1fe27f199ac63..cfdc03341e8bc 100644
--- a/sklearn/utils/tests/test_validation.py
+++ b/sklearn/utils/tests/test_validation.py
@@ -433,6 +433,46 @@ def test_check_array_min_samples_and_features_messages():
     assert_array_equal(y, y_checked)
 
 
+def test_check_array_complex_data_error():
+    # np array
+    X = np.array([[1 + 2j, 3 + 4j, 5 + 7j], [2 + 3j, 4 + 5j, 6 + 7j]])
+    assert_raises_regexp(
+        ValueError, "Complex data not supported", check_array, X)
+
+    # list of lists
+    X = [[1 + 2j, 3 + 4j, 5 + 7j], [2 + 3j, 4 + 5j, 6 + 7j]]
+    assert_raises_regexp(
+        ValueError, "Complex data not supported", check_array, X)
+
+    # tuple of tuples
+    X = ((1 + 2j, 3 + 4j, 5 + 7j), (2 + 3j, 4 + 5j, 6 + 7j))
+    assert_raises_regexp(
+        ValueError, "Complex data not supported", check_array, X)
+
+    # list of np arrays
+    X = [np.array([1 + 2j, 3 + 4j, 5 + 7j]),
+         np.array([2 + 3j, 4 + 5j, 6 + 7j])]
+    assert_raises_regexp(
+        ValueError, "Complex data not supported", check_array, X)
+
+    # tuple of np arrays
+    X = (np.array([1 + 2j, 3 + 4j, 5 + 7j]),
+         np.array([2 + 3j, 4 + 5j, 6 + 7j]))
+    assert_raises_regexp(
+        ValueError, "Complex data not supported", check_array, X)
+
+    # dataframe
+    X = MockDataFrame(
+        np.array([[1 + 2j, 3 + 4j, 5 + 7j], [2 + 3j, 4 + 5j, 6 + 7j]]))
+    assert_raises_regexp(
+        ValueError, "Complex data not supported", check_array, X)
+
+    # sparse matrix
+    X = sp.coo_matrix([[0, 1 + 2j], [0, 0]])
+    assert_raises_regexp(
+        ValueError, "Complex data not supported", check_array, X)
+
+
 def test_has_fit_parameter():
     assert_false(has_fit_parameter(KNeighborsClassifier, "sample_weight"))
     assert_true(has_fit_parameter(RandomForestRegressor, "sample_weight"))
diff --git a/sklearn/utils/validation.py b/sklearn/utils/validation.py
index 460f20673feaf..4af88a7ed9bb6 100644
--- a/sklearn/utils/validation.py
+++ b/sklearn/utils/validation.py
@@ -13,6 +13,7 @@
 
 import numpy as np
 import scipy.sparse as sp
+from numpy.core.numeric import ComplexWarning
 
 from ..externals import six
 from ..utils.fixes import signature
@@ -276,6 +277,13 @@ def _ensure_sparse_format(spmatrix, accept_sparse, dtype, copy,
     return spmatrix
 
 
+def _ensure_no_complex_data(array):
+    if hasattr(array, 'dtype') and array.dtype is not None \
+            and hasattr(array.dtype, 'kind') and array.dtype.kind == "c":
+        raise ValueError("Complex data not supported\n"
+                         "{}\n".format(array))
+
+
 def check_array(array, accept_sparse=False, dtype="numeric", order=None,
                 copy=False, force_all_finite=True, ensure_2d=True,
                 allow_nd=False, ensure_min_samples=1, ensure_min_features=1,
@@ -396,10 +404,28 @@ def check_array(array, accept_sparse=False, dtype="numeric", order=None,
     context = " by %s" % estimator_name if estimator is not None else ""
 
     if sp.issparse(array):
+        _ensure_no_complex_data(array)
         array = _ensure_sparse_format(array, accept_sparse, dtype, copy,
                                       force_all_finite)
     else:
-        array = np.array(array, dtype=dtype, order=order, copy=copy)
+        # If np.array(..) gives ComplexWarning, then we convert the warning
+        # to an error. This is needed because specifying a non complex
+        # dtype to the function converts complex to real dtype,
+        # thereby passing the test made in the lines following the scope
+        # of warnings context manager.
+        with warnings.catch_warnings():
+            try:
+                warnings.simplefilter('error', ComplexWarning)
+                array = np.array(array, dtype=dtype, order=order, copy=copy)
+            except ComplexWarning:
+                raise ValueError("Complex data not supported\n"
+                                 "{}\n".format(array))
+
+        # It is possible that the np.array(..) gave no warning. This happens
+        # when no dtype conversion happend, for example dtype = None. The
+        # result is that np.array(..) produces an array of complex dtype
+        # and we need to catch and raise exception for such cases.
+        _ensure_no_complex_data(array)
 
         if ensure_2d:
             if array.ndim == 1: