diff --git a/doc/source/whatsnew/v1.0.0.rst b/doc/source/whatsnew/v1.0.0.rst
index cc4bab8b9a923..a266f79aed02c 100644
--- a/doc/source/whatsnew/v1.0.0.rst
+++ b/doc/source/whatsnew/v1.0.0.rst
@@ -166,6 +166,7 @@ Groupby/resample/rolling
 
 -
 -
+- Bug in :meth:`DataFrame.groupby` not offering selection by column name when ``axis=1`` (:issue:`27614`)
 
 Reshaping
 ^^^^^^^^^
diff --git a/pandas/core/groupby/grouper.py b/pandas/core/groupby/grouper.py
index 1d88ebd26b1b6..5c32550af3883 100644
--- a/pandas/core/groupby/grouper.py
+++ b/pandas/core/groupby/grouper.py
@@ -606,10 +606,10 @@ def is_in_obj(gpr):
         elif is_in_axis(gpr):  # df.groupby('name')
             if gpr in obj:
                 if validate:
-                    obj._check_label_or_level_ambiguity(gpr)
+                    obj._check_label_or_level_ambiguity(gpr, axis=axis)
                 in_axis, name, gpr = True, gpr, obj[gpr]
                 exclusions.append(name)
-            elif obj._is_level_reference(gpr):
+            elif obj._is_level_reference(gpr, axis=axis):
                 in_axis, name, level, gpr = False, None, gpr, None
             else:
                 raise KeyError(gpr)
diff --git a/pandas/tests/groupby/test_groupby.py b/pandas/tests/groupby/test_groupby.py
index 2379d25ebe5aa..4556b22b57279 100644
--- a/pandas/tests/groupby/test_groupby.py
+++ b/pandas/tests/groupby/test_groupby.py
@@ -1860,3 +1860,25 @@ def test_groupby_groups_in_BaseGrouper():
     result = df.groupby(["beta", pd.Grouper(level="alpha")])
     expected = df.groupby(["beta", "alpha"])
     assert result.groups == expected.groups
+
+
+@pytest.mark.parametrize("group_name", ["x", ["x"]])
+def test_groupby_axis_1(group_name):
+    # GH 27614
+    df = pd.DataFrame(
+        np.arange(12).reshape(3, 4), index=[0, 1, 0], columns=[10, 20, 10, 20]
+    )
+    df.index.name = "y"
+    df.columns.name = "x"
+
+    results = df.groupby(group_name, axis=1).sum()
+    expected = df.T.groupby(group_name).sum().T
+    assert_frame_equal(results, expected)
+
+    # test on MI column
+    iterables = [["bar", "baz", "foo"], ["one", "two"]]
+    mi = pd.MultiIndex.from_product(iterables=iterables, names=["x", "x1"])
+    df = pd.DataFrame(np.arange(18).reshape(3, 6), index=[0, 1, 0], columns=mi)
+    results = df.groupby(group_name, axis=1).sum()
+    expected = df.T.groupby(group_name).sum().T
+    assert_frame_equal(results, expected)