diff --git a/geopandas/geodataframe.py b/geopandas/geodataframe.py
index ab92ed7..4b16d7f 100644
--- a/geopandas/geodataframe.py
+++ b/geopandas/geodataframe.py
@@ -157,7 +157,6 @@ class GeoDataFrame(GeoPandasBase, DataFrame):
                 )
 
             # only if we have actual geometry values -> call set_geometry
-            index = self.index
             try:
                 if (
                     hasattr(self["geometry"].values, "crs")
@@ -170,11 +169,6 @@ class GeoDataFrame(GeoPandasBase, DataFrame):
             except TypeError:
                 pass
             else:
-                if self.index is not index:
-                    # With pandas < 1.0 and an empty frame (no rows), the index
-                    # gets reset to a default RangeIndex -> set back the original
-                    # index if needed
-                    self.index = index
                 geometry = "geometry"
 
         if geometry is not None:
@@ -346,12 +340,7 @@ class GeoDataFrame(GeoPandasBase, DataFrame):
 
         # Check that we are using a listlike of geometries
         level = _ensure_geometry(level, crs=crs)
-        index = frame.index
         frame[geo_column_name] = level
-        if frame.index is not index and len(frame.index) == len(index):
-            # With pandas < 1.0 and an empty frame (no rows), the index gets reset
-            # to a default RangeIndex -> set back the original index if needed
-            frame.index = index
         frame._geometry_column_name = geo_column_name
         frame.crs = crs
         if not inplace:
diff --git a/geopandas/tests/test_pandas_methods.py b/geopandas/tests/test_pandas_methods.py
index 4d2ed82..252af1d 100644
--- a/geopandas/tests/test_pandas_methods.py
+++ b/geopandas/tests/test_pandas_methods.py
@@ -268,7 +268,7 @@ def test_convert_dtypes(df):
 
     # Test geometry col is first col, first, geom_col_name=geometry
     # (order is important in concat, used internally)
-    res1 = df.convert_dtypes()  # note res1 done first for pandas < 1 xfail check
+    res1 = df.convert_dtypes()
 
     expected1 = GeoDataFrame(
         pd.DataFrame(df).convert_dtypes(), crs=df.crs, geometry=df.geometry.name