diff --git a/pandas/io/excel.py b/pandas/io/excel.py
index 6b7c597ecfcdc..f34ba65cf7b51 100644
--- a/pandas/io/excel.py
+++ b/pandas/io/excel.py
@@ -788,9 +788,15 @@ def __init__(self, path, engine=None, **engine_kwargs):
 
         # Create workbook object with default optimized_write=True.
         self.book = Workbook()
+
         # Openpyxl 1.6.1 adds a dummy sheet. We remove it.
         if self.book.worksheets:
-            self.book.remove_sheet(self.book.worksheets[0])
+            try:
+                self.book.remove(self.book.worksheets[0])
+            except AttributeError:
+
+                # compat
+                self.book.remove_sheet(self.book.worksheets[0])
 
     def save(self):
         """
@@ -911,7 +917,7 @@ def write_cells(self, cells, sheet_name=None, startrow=0, startcol=0):
 
         for cell in cells:
             colletter = get_column_letter(startcol + cell.col + 1)
-            xcell = wks.cell("%s%s" % (colletter, startrow + cell.row + 1))
+            xcell = wks["%s%s" % (colletter, startrow + cell.row + 1)]
             xcell.value = _conv_value(cell.val)
             style_kwargs = {}
 
@@ -952,7 +958,7 @@ def write_cells(self, cells, sheet_name=None, startrow=0, startcol=0):
                                 # Ignore first cell. It is already handled.
                                 continue
                             colletter = get_column_letter(col)
-                            xcell = wks.cell("%s%s" % (colletter, row))
+                            xcell = wks["%s%s" % (colletter, row)]
                             xcell.style = xcell.style.copy(**style_kwargs)
 
     @classmethod
diff --git a/pandas/io/tests/test_excel.py b/pandas/io/tests/test_excel.py
index 9dd2739608b7a..a2162320d9d1b 100644
--- a/pandas/io/tests/test_excel.py
+++ b/pandas/io/tests/test_excel.py
@@ -2006,8 +2006,8 @@ def test_write_cells_merge_styled(self):
             writer.write_cells(merge_cells, sheet_name=sheet_name)
 
             wks = writer.sheets[sheet_name]
-            xcell_b1 = wks.cell('B1')
-            xcell_a2 = wks.cell('A2')
+            xcell_b1 = wks['B1']
+            xcell_a2 = wks['A2']
             self.assertEqual(xcell_b1.style, openpyxl_sty_merged)
             self.assertEqual(xcell_a2.style, openpyxl_sty_merged)
 
@@ -2118,8 +2118,8 @@ def test_write_cells_merge_styled(self):
             writer.write_cells(merge_cells, sheet_name=sheet_name)
 
             wks = writer.sheets[sheet_name]
-            xcell_b1 = wks.cell('B1')
-            xcell_a2 = wks.cell('A2')
+            xcell_b1 = wks['B1']
+            xcell_a2 = wks['A2']
             self.assertEqual(xcell_b1.font, openpyxl_sty_merged)
             self.assertEqual(xcell_a2.font, openpyxl_sty_merged)
 
@@ -2213,11 +2213,18 @@ def test_column_format(self):
             writer.save()
 
             read_workbook = openpyxl.load_workbook(path)
-            read_worksheet = read_workbook.get_sheet_by_name(name='Sheet1')
+            try:
+                read_worksheet = read_workbook['Sheet1']
+            except TypeError:
+                # compat
+                read_worksheet = read_workbook.get_sheet_by_name(name='Sheet1')
 
-            # Get the number format from the cell. This method is backward
-            # compatible with older versions of openpyxl.
-            cell = read_worksheet.cell('B2')
+            # Get the number format from the cell.
+            try:
+                cell = read_worksheet['B2']
+            except TypeError:
+                # compat
+                cell = read_worksheet.cell('B2')
 
             try:
                 read_num_format = cell.number_format