diff --git a/doc/source/whatsnew/v0.24.0.rst b/doc/source/whatsnew/v0.24.0.rst
index 960b205c49c617..dd06bade2a2038 100644
--- a/doc/source/whatsnew/v0.24.0.rst
+++ b/doc/source/whatsnew/v0.24.0.rst
@@ -1639,6 +1639,7 @@ Conversion
 - Bug in :meth:`DataFrame.combine_first` in which column types were unexpectedly converted to float (:issue:`20699`)
 - Bug in :meth:`DataFrame.clip` in which column types are not preserved and casted to float (:issue:`24162`)
 - Bug in :meth:`DataFrame.clip` when order of columns of dataframes doesn't match, result observed is wrong in numeric values (:issue:`20911`)
+- Bug in :meth:`DataFrame.astype` where converting to an extension dtype when duplicate column names are present causes a ``RecursionError`` (:issue:`24704`)
 
 Strings
 ^^^^^^^
diff --git a/pandas/core/generic.py b/pandas/core/generic.py
index 1e6ae716606179..a0ee9cb253fef0 100644
--- a/pandas/core/generic.py
+++ b/pandas/core/generic.py
@@ -5670,9 +5670,10 @@ def astype(self, dtype, copy=True, errors='raise', **kwargs):
                     results.append(results.append(col.copy() if copy else col))
 
         elif is_extension_array_dtype(dtype) and self.ndim > 1:
-            # GH 18099: columnwise conversion to categorical
-            # and extension dtype
-            results = (self[col].astype(dtype, copy=copy) for col in self)
+            # GH 18099/22869: columnwise conversion to extension dtype
+            # GH 24704: use iloc to handle duplicate column names
+            results = (self.iloc[:, i].astype(dtype, copy=copy)
+                       for i in range(len(self.columns)))
 
         else:
             # else, only a single dtype is given
diff --git a/pandas/tests/frame/test_dtypes.py b/pandas/tests/frame/test_dtypes.py
index 70de148dd8fd28..a9f8ab47b16de2 100644
--- a/pandas/tests/frame/test_dtypes.py
+++ b/pandas/tests/frame/test_dtypes.py
@@ -709,6 +709,17 @@ def test_astype_extension_dtypes_1d(self, dtype):
         tm.assert_frame_equal(df.astype(dtype), expected1)
         tm.assert_frame_equal(df.astype('int64').astype(dtype), expected1)
 
+    @pytest.mark.parametrize("dtype", ['category', 'Int64'])
+    def test_astype_extension_dtypes_duplicate_col(self, dtype):
+        # GH 24704
+        a1 = Series([0, np.nan, 4], name='a')
+        a2 = Series([np.nan, 3, 5], name='a')
+        df = concat([a1, a2], axis=1)
+
+        result = df.astype(dtype)
+        expected = concat([a1.astype(dtype), a2.astype(dtype)], axis=1)
+        assert_frame_equal(result, expected)
+
     @pytest.mark.parametrize('dtype', [
         {100: 'float64', 200: 'uint64'}, 'category', 'float64'])
     def test_astype_column_metadata(self, dtype):