diff --git a/doc/source/whatsnew/v1.0.0.rst b/doc/source/whatsnew/v1.0.0.rst
old mode 100644
new mode 100755
index d0dc3f58379a0..0f0d86e271061
--- a/doc/source/whatsnew/v1.0.0.rst
+++ b/doc/source/whatsnew/v1.0.0.rst
@@ -824,7 +824,7 @@ Groupby/resample/rolling
 - Bug in :meth:`DataFrameGroupBy.rolling().quantile()` ignoring ``interpolation`` keyword argument (:issue:`28779`)
 - Bug in :meth:`DataFrame.groupby` where ``any``, ``all``, ``nunique`` and transform functions would incorrectly handle duplicate column labels (:issue:`21668`)
 - Bug in :meth:`DataFrameGroupBy.agg` with timezone-aware datetime64 column incorrectly casting results to the original dtype (:issue:`29641`)
--
+- Bug in :meth:`DataFrame.groupby` when using axis=1 and having a single level columns index (:issue:`30208`)
 
 Reshaping
 ^^^^^^^^^
diff --git a/pandas/core/groupby/grouper.py b/pandas/core/groupby/grouper.py
index b0df04f18ff1d..18b08f191770f 100644
--- a/pandas/core/groupby/grouper.py
+++ b/pandas/core/groupby/grouper.py
@@ -491,8 +491,11 @@ def get_grouper(
                     raise ValueError("multiple levels only valid with MultiIndex")
 
             if isinstance(level, str):
-                if obj.index.name != level:
-                    raise ValueError(f"level name {level} is not the name of the index")
+                if obj._get_axis(axis).name != level:
+                    raise ValueError(
+                        f"level name {level} is not the name "
+                        f"of the {obj._get_axis_name(axis)}"
+                    )
             elif level > 0 or level < -1:
                 raise ValueError("level > 0 or level < -1 only valid with MultiIndex")
 
diff --git a/pandas/tests/groupby/test_grouping.py b/pandas/tests/groupby/test_grouping.py
index 2c84c2f034fc6..f2af397357e4f 100644
--- a/pandas/tests/groupby/test_grouping.py
+++ b/pandas/tests/groupby/test_grouping.py
@@ -501,15 +501,17 @@ def test_groupby_level(self, sort, mframe, df):
         with pytest.raises(ValueError, match=msg):
             df.groupby(level=1)
 
-    def test_groupby_level_index_names(self):
+    def test_groupby_level_index_names(self, axis):
         # GH4014 this used to raise ValueError since 'exp'>1 (in py2)
         df = DataFrame({"exp": ["A"] * 3 + ["B"] * 3, "var1": range(6)}).set_index(
             "exp"
         )
-        df.groupby(level="exp")
-        msg = "level name foo is not the name of the index"
+        if axis in (1, "columns"):
+            df = df.T
+        df.groupby(level="exp", axis=axis)
+        msg = f"level name foo is not the name of the {df._get_axis_name(axis)}"
         with pytest.raises(ValueError, match=msg):
-            df.groupby(level="foo")
+            df.groupby(level="foo", axis=axis)
 
     @pytest.mark.parametrize("sort", [True, False])
     def test_groupby_level_with_nas(self, sort):