diff --git a/django/db/models/fields/__init__.py b/django/db/models/fields/__init__.py
index f9ae55f844..3351b4ad35 100644
--- a/django/db/models/fields/__init__.py
+++ b/django/db/models/fields/__init__.py
@@ -1069,11 +1069,7 @@ class CharField(Field):
         return errors
 
     def _check_max_length_attribute(self, **kwargs):
-        try:
-            max_length = int(self.max_length)
-            if max_length <= 0:
-                raise ValueError()
-        except TypeError:
+        if self.max_length is None:
             return [
                 checks.Error(
                     "CharFields must define a 'max_length' attribute.",
@@ -1082,7 +1078,7 @@ class CharField(Field):
                     id='fields.E120',
                 )
             ]
-        except ValueError:
+        elif not isinstance(self.max_length, six.integer_types) or self.max_length <= 0:
             return [
                 checks.Error(
                     "'max_length' must be a positive integer.",
diff --git a/tests/invalid_models_tests/test_ordinary_fields.py b/tests/invalid_models_tests/test_ordinary_fields.py
index c98d218b09..9baaf70feb 100644
--- a/tests/invalid_models_tests/test_ordinary_fields.py
+++ b/tests/invalid_models_tests/test_ordinary_fields.py
@@ -129,6 +129,22 @@ class CharFieldTests(IsolatedModelsTestCase):
         ]
         self.assertEqual(errors, expected)
 
+    def test_str_max_length_value(self):
+        class Model(models.Model):
+            field = models.CharField(max_length='20')
+
+        field = Model._meta.get_field('field')
+        errors = field.check()
+        expected = [
+            Error(
+                "'max_length' must be a positive integer.",
+                hint=None,
+                obj=field,
+                id='fields.E121',
+            ),
+        ]
+        self.assertEqual(errors, expected)
+
     def test_non_iterable_choices(self):
         class Model(models.Model):
             field = models.CharField(max_length=10, choices='bad')