diff --git a/pandas/core/frame.py b/pandas/core/frame.py
index ffb2ad046158f..a0559cef6831d 100644
--- a/pandas/core/frame.py
+++ b/pandas/core/frame.py
@@ -4354,6 +4354,9 @@ def duplicated(self, subset=None, keep='first'):
         from pandas.core.sorting import get_group_index
         from pandas._libs.hashtable import duplicated_int64, _SIZE_HINT_LIMIT
 
+        if self.columns.empty:
+            return Series()
+
         def f(vals):
             labels, shape = algorithms.factorize(
                 vals, size_hint=min(len(self), _SIZE_HINT_LIMIT))
diff --git a/pandas/tests/frame/test_analytics.py b/pandas/tests/frame/test_analytics.py
index d1a4a5f615b86..66a5c181b1369 100644
--- a/pandas/tests/frame/test_analytics.py
+++ b/pandas/tests/frame/test_analytics.py
@@ -1522,6 +1522,16 @@ def test_drop_duplicates_with_duplicate_column_names(self):
         expected1 = df[:2]
         tm.assert_frame_equal(result1, expected1)
 
+    def test_drop_duplicates_with_no_column(self):
+        # GH20516
+        df0 = DataFrame()
+        result0 = df0.drop_duplicates()
+        tm.assert_frame_equal(result0, df0)
+
+        df1 = DataFrame(index=[1, 2])
+        result1 = df1.drop_duplicates()
+        tm.assert_frame_equal(result1, df1)
+
     def test_drop_duplicates_for_take_all(self):
         df = DataFrame({'AAA': ['foo', 'bar', 'baz', 'bar',
                                 'foo', 'bar', 'qux', 'foo'],