diff --git a/doc/source/whatsnew/v1.1.0.rst b/doc/source/whatsnew/v1.1.0.rst
index 4044fb2d3fa09..193dda97c31b7 100644
--- a/doc/source/whatsnew/v1.1.0.rst
+++ b/doc/source/whatsnew/v1.1.0.rst
@@ -349,6 +349,7 @@ I/O
 - Bug in :meth:`read_csv` was causing a file descriptor leak on an empty file (:issue:`31488`)
 - Bug in :meth:`read_csv` was causing a segfault when there were blank lines between the header and data rows (:issue:`28071`)
 - Bug in :meth:`read_csv` was raising a misleading exception on a permissions issue (:issue:`23784`)
+- Bug in :meth:`read_csv` was raising an ``IndexError`` when header=None and 2 extra data columns
 
 
 Plotting
diff --git a/pandas/_libs/parsers.pyx b/pandas/_libs/parsers.pyx
index 2085e91d69ed0..c6b68d9a0ab5c 100644
--- a/pandas/_libs/parsers.pyx
+++ b/pandas/_libs/parsers.pyx
@@ -1316,8 +1316,8 @@ cdef class TextReader:
         else:
             if self.header is not None:
                 j = i - self.leading_cols
-                # hack for #2442
-                if j == len(self.header[0]):
+                # generate extra (bogus) headers if there are more columns than headers
+                if j >= len(self.header[0]):
                     return j
                 else:
                     return self.header[0][j]
diff --git a/pandas/tests/io/parser/test_common.py b/pandas/tests/io/parser/test_common.py
index 4a9fa61bc4233..5bf9587a6ca22 100644
--- a/pandas/tests/io/parser/test_common.py
+++ b/pandas/tests/io/parser/test_common.py
@@ -2116,3 +2116,13 @@ def test_blank_lines_between_header_and_data_rows(all_parsers, nrows):
     parser = all_parsers
     df = parser.read_csv(StringIO(csv), header=3, nrows=nrows, skip_blank_lines=False)
     tm.assert_frame_equal(df, ref[:nrows])
+
+
+def test_no_header_two_extra_columns(all_parsers):
+    # GH 26218
+    column_names = ["one", "two", "three"]
+    ref = DataFrame([["foo", "bar", "baz"]], columns=column_names)
+    stream = StringIO("foo,bar,baz,bam,blah")
+    parser = all_parsers
+    df = parser.read_csv(stream, header=None, names=column_names, index_col=False)
+    tm.assert_frame_equal(df, ref)