diff --git a/django/forms/fields.py b/django/forms/fields.py
index c06352a964..7a59a3d664 100644
--- a/django/forms/fields.py
+++ b/django/forms/fields.py
@@ -279,6 +279,15 @@ class FloatField(IntegerField):
             raise ValidationError(self.error_messages['invalid'], code='invalid')
         return value
 
+    def validate(self, value):
+        super(FloatField, self).validate(value)
+
+        # Check for NaN (which is the only thing not equal to itself) and +/- infinity
+        if value != value or value in (Decimal('Inf'), Decimal('-Inf')):
+            raise ValidationError(self.error_messages['invalid'], code='invalid')
+
+        return value
+
     def widget_attrs(self, widget):
         attrs = super(FloatField, self).widget_attrs(widget)
         if isinstance(widget, NumberInput):
diff --git a/tests/forms_tests/tests/test_fields.py b/tests/forms_tests/tests/test_fields.py
index a4e81d31ae..6f305d78c4 100644
--- a/tests/forms_tests/tests/test_fields.py
+++ b/tests/forms_tests/tests/test_fields.py
@@ -254,6 +254,9 @@ class FieldsTests(SimpleTestCase):
         self.assertRaisesMessage(ValidationError, "'Enter a number.'", f.clean, '1.0a')
         self.assertEqual(f.max_value, None)
         self.assertEqual(f.min_value, None)
+        self.assertRaisesMessage(ValidationError, "'Enter a number.'", f.clean, 'Infinity')
+        self.assertRaisesMessage(ValidationError, "'Enter a number.'", f.clean, 'NaN')
+        self.assertRaisesMessage(ValidationError, "'Enter a number.'", f.clean, '-Inf')
 
     def test_floatfield_2(self):
         f = FloatField(required=False)