diff --git a/doc/source/whatsnew/v1.4.0.rst b/doc/source/whatsnew/v1.4.0.rst
index 39e3894f86302..693923522e437 100644
--- a/doc/source/whatsnew/v1.4.0.rst
+++ b/doc/source/whatsnew/v1.4.0.rst
@@ -653,7 +653,7 @@ I/O
 - Bug in unpickling a :class:`Index` with object dtype incorrectly inferring numeric dtypes (:issue:`43188`)
 - Bug in :func:`read_csv` where reading multi-header input with unequal lengths incorrectly raising uncontrolled ``IndexError`` (:issue:`43102`)
 - Bug in :func:`read_csv`, changed exception class when expecting a file path name or file-like object from ``OSError`` to ``TypeError`` (:issue:`43366`)
-- Bug in :func:`read_csv` and :func:`read_fwf` ignoring all ``skiprows`` except first when ``nrows`` is specified for ``engine='python'`` (:issue:`44021`)
+- Bug in :func:`read_csv` and :func:`read_fwf` ignoring all ``skiprows`` except first when ``nrows`` is specified for ``engine='python'`` (:issue:`44021`, :issue:`10261`)
 - Bug in :func:`read_json` not handling non-numpy dtypes correctly (especially ``category``) (:issue:`21892`, :issue:`33205`)
 - Bug in :func:`json_normalize` where multi-character ``sep`` parameter is incorrectly prefixed to every key (:issue:`43831`)
 - Bug in :func:`json_normalize` where reading data with missing multi-level metadata would not respect errors="ignore" (:issue:`44312`)
diff --git a/pandas/io/parsers/python_parser.py b/pandas/io/parsers/python_parser.py
index f5420618c0235..153ba171199e6 100644
--- a/pandas/io/parsers/python_parser.py
+++ b/pandas/io/parsers/python_parser.py
@@ -1048,6 +1048,7 @@ def _get_lines(self, rows=None):
                             assert self.data is not None
                             new_rows.append(next(self.data))
 
+                        len_new_rows = len(new_rows)
                         new_rows = self._remove_skipped_rows(new_rows)
                         lines.extend(new_rows)
                     else:
@@ -1059,13 +1060,15 @@ def _get_lines(self, rows=None):
 
                             if new_row is not None:
                                 new_rows.append(new_row)
+                        len_new_rows = len(new_rows)
 
                 except StopIteration:
+                    len_new_rows = len(new_rows)
                     new_rows = self._remove_skipped_rows(new_rows)
                     lines.extend(new_rows)
                     if len(lines) == 0:
                         raise
-                self.pos += len(new_rows)
+                self.pos += len_new_rows
 
             self.buf = []
         else:
diff --git a/pandas/tests/io/parser/test_read_fwf.py b/pandas/tests/io/parser/test_read_fwf.py
index 910731bd7dde2..3f43ea0b8a12d 100644
--- a/pandas/tests/io/parser/test_read_fwf.py
+++ b/pandas/tests/io/parser/test_read_fwf.py
@@ -877,3 +877,33 @@ def test_skip_rows_and_n_rows():
     result = read_fwf(StringIO(data), nrows=4, skiprows=[2, 4])
     expected = DataFrame({"a": [1, 3, 5, 6], "b": ["a", "c", "e", "f"]})
     tm.assert_frame_equal(result, expected)
+
+
+def test_skiprows_with_iterator():
+    # GH#10261
+    data = """0
+1
+2
+3
+4
+5
+6
+7
+8
+9
+    """
+    df_iter = read_fwf(
+        StringIO(data),
+        colspecs=[(0, 2)],
+        names=["a"],
+        iterator=True,
+        chunksize=2,
+        skiprows=[0, 1, 2, 6, 9],
+    )
+    expected_frames = [
+        DataFrame({"a": [3, 4]}),
+        DataFrame({"a": [5, 7, 8]}, index=[2, 3, 4]),
+        DataFrame({"a": []}, index=[], dtype="object"),
+    ]
+    for i, result in enumerate(df_iter):
+        tm.assert_frame_equal(result, expected_frames[i])