diff --git a/sklearn/grid_search.py b/sklearn/grid_search.py
index 7539dc8a33a6c..202327574ee76 100644
--- a/sklearn/grid_search.py
+++ b/sklearn/grid_search.py
@@ -326,17 +326,18 @@ def _check_param_grid(param_grid):
         param_grid = [param_grid]
 
     for p in param_grid:
-        for v in p.values():
+        for name, v in p.items():
             if isinstance(v, np.ndarray) and v.ndim > 1:
                 raise ValueError("Parameter array should be one-dimensional.")
 
             check = [isinstance(v, k) for k in (list, tuple, np.ndarray)]
             if True not in check:
-                raise ValueError("Parameter values should be a list.")
+                raise ValueError("Parameter values for parameter ({0}) need "
+                                 "to be a sequence.".format(name))
 
             if len(v) == 0:
-                raise ValueError("Parameter values should be a non-empty "
-                                 "list.")
+                raise ValueError("Parameter values for parameter ({0}) need "
+                                 "to be a non-empty sequence.".format(name))
 
 
 class _CVScoreTuple (namedtuple('_CVScoreTuple',
diff --git a/sklearn/model_selection/_search.py b/sklearn/model_selection/_search.py
index df0f721d109db..d433ca15b823d 100644
--- a/sklearn/model_selection/_search.py
+++ b/sklearn/model_selection/_search.py
@@ -327,17 +327,18 @@ def _check_param_grid(param_grid):
         param_grid = [param_grid]
 
     for p in param_grid:
-        for v in p.values():
+        for name, v in p.items():
             if isinstance(v, np.ndarray) and v.ndim > 1:
                 raise ValueError("Parameter array should be one-dimensional.")
 
             check = [isinstance(v, k) for k in (list, tuple, np.ndarray)]
             if True not in check:
-                raise ValueError("Parameter values should be a list.")
+                raise ValueError("Parameter values for parameter ({0}) need "
+                                 "to be a sequence.".format(name))
 
             if len(v) == 0:
-                raise ValueError("Parameter values should be a non-empty "
-                                 "list.")
+                raise ValueError("Parameter values for parameter ({0}) need "
+                                 "to be a non-empty sequence.".format(name))
 
 
 # XXX Remove in 0.20
diff --git a/sklearn/model_selection/tests/test_search.py b/sklearn/model_selection/tests/test_search.py
index 75e0d5f71cb40..6bb5752e85262 100644
--- a/sklearn/model_selection/tests/test_search.py
+++ b/sklearn/model_selection/tests/test_search.py
@@ -165,6 +165,22 @@ def test_grid_search():
     assert_raises(ValueError, grid_search.fit, X, y)
 
 
+def test_grid_search_incorrect_param_grid():
+    clf = MockClassifier()
+    assert_raise_message(
+        ValueError,
+        "Parameter values for parameter (C) need to be a sequence.",
+        GridSearchCV, clf, {'C': 1})
+
+
+def test_grid_search_param_grid_includes_sequence_of_a_zero_length():
+    clf = MockClassifier()
+    assert_raise_message(
+        ValueError,
+        "Parameter values for parameter (C) need to be a non-empty sequence.",
+        GridSearchCV, clf, {'C': []})
+
+
 @ignore_warnings
 def test_grid_search_no_score():
     # Test grid-search on classifier that has no score function.