diff --git a/lib/matplotlib/tests/test_simplification.py b/lib/matplotlib/tests/test_simplification.py
index 0a5c215eff30..a052c24cb655 100644
--- a/lib/matplotlib/tests/test_simplification.py
+++ b/lib/matplotlib/tests/test_simplification.py
@@ -518,3 +518,54 @@ def test_clipping_full():
     simplified = list(p.iter_segments(clip=[0, 0, 100, 100]))
     assert ([(list(x), y) for x, y in simplified] ==
             [([50, 40], 1)])
+
+
+def test_simplify_closepoly():
+    # The values of the vertices in a CLOSEPOLY should always be ignored,
+    # in favor of the most recent MOVETO's vertex values
+    paths = [Path([(1, 1), (2, 1), (2, 2), (np.nan, np.nan)],
+                  [Path.MOVETO, Path.LINETO, Path.LINETO, Path.CLOSEPOLY]),
+             Path([(1, 1), (2, 1), (2, 2), (40, 50)],
+                  [Path.MOVETO, Path.LINETO, Path.LINETO, Path.CLOSEPOLY])]
+    expected_path = Path([(1, 1), (2, 1), (2, 2), (1, 1), (1, 1), (0, 0)],
+                         [Path.MOVETO, Path.LINETO, Path.LINETO, Path.LINETO,
+                          Path.LINETO, Path.STOP])
+
+    for path in paths:
+        simplified_path = path.cleaned(simplify=True)
+        assert_array_equal(expected_path.vertices, simplified_path.vertices)
+        assert_array_equal(expected_path.codes, simplified_path.codes)
+
+    # test that a compound path also works
+    path = Path([(1, 1), (2, 1), (2, 2), (np.nan, np.nan),
+                 (-1, 0), (-2, 0), (-2, 1), (np.nan, np.nan)],
+                [Path.MOVETO, Path.LINETO, Path.LINETO, Path.CLOSEPOLY,
+                 Path.MOVETO, Path.LINETO, Path.LINETO, Path.CLOSEPOLY])
+    expected_path = Path([(1, 1), (2, 1), (2, 2), (1, 1),
+                          (-1, 0), (-2, 0), (-2, 1), (-1, 0), (-1, 0), (0, 0)],
+                         [Path.MOVETO, Path.LINETO, Path.LINETO, Path.LINETO,
+                          Path.MOVETO, Path.LINETO, Path.LINETO, Path.LINETO,
+                          Path.LINETO, Path.STOP])
+
+    simplified_path = path.cleaned(simplify=True)
+    assert_array_equal(expected_path.vertices, simplified_path.vertices)
+    assert_array_equal(expected_path.codes, simplified_path.codes)
+
+    # test for a path with an invalid MOVETO
+    # CLOSEPOLY with an invalid MOVETO should be ignored
+    path = Path([(1, 0), (1, -1), (2, -1),
+                 (np.nan, np.nan), (-1, -1), (-2, 1), (-1, 1),
+                 (2, 2), (0, -1)],
+                [Path.MOVETO, Path.LINETO, Path.LINETO,
+                 Path.MOVETO, Path.LINETO, Path.LINETO, Path.LINETO,
+                 Path.CLOSEPOLY, Path.LINETO])
+    expected_path = Path([(1, 0), (1, -1), (2, -1),
+                          (np.nan, np.nan), (-1, -1), (-2, 1), (-1, 1),
+                          (0, -1), (0, -1), (0, 0)],
+                         [Path.MOVETO, Path.LINETO, Path.LINETO,
+                          Path.MOVETO, Path.LINETO, Path.LINETO, Path.LINETO,
+                          Path.LINETO, Path.LINETO, Path.STOP])
+
+    simplified_path = path.cleaned(simplify=True)
+    assert_array_equal(expected_path.vertices, simplified_path.vertices)
+    assert_array_equal(expected_path.codes, simplified_path.codes)
diff --git a/src/path_converters.h b/src/path_converters.h
index db732e126c3f..a78643d64ed5 100644
--- a/src/path_converters.h
+++ b/src/path_converters.h
@@ -644,6 +644,13 @@ class PathSimplifier : protected EmbeddedQueue<9>
           m_after_moveto(false),
           m_clipped(false),
 
+          // whether the most recent MOVETO vertex is valid
+          m_has_init(false),
+
+          // the most recent MOVETO vertex
+          m_initX(0.0),
+          m_initY(0.0),
+
           // the x, y values from last iteration
           m_lastx(0.0),
           m_lasty(0.0),
@@ -754,6 +761,15 @@ class PathSimplifier : protected EmbeddedQueue<9>
                     _push(x, y);
                 }
                 m_after_moveto = true;
+
+                if (std::isfinite(*x) && std::isfinite(*y)) {
+                    m_has_init = true;
+                    m_initX = *x;
+                    m_initY = *y;
+                } else {
+                    m_has_init = false;
+                }
+
                 m_lastx = *x;
                 m_lasty = *y;
                 m_moveto = false;
@@ -768,6 +784,19 @@ class PathSimplifier : protected EmbeddedQueue<9>
             }
             m_after_moveto = false;
 
+            if(agg::is_close(cmd)) {
+                if (m_has_init) {
+                    /* If we have a valid initial vertex, then
+                       replace the current vertex with the initial vertex */
+                    *x = m_initX;
+                    *y = m_initY;
+                } else {
+                    /* If we don't have a valid initial vertex, then
+                       we can't close the path, so we skip the vertex */
+                    continue;
+                }
+            }
+
             /* NOTE: We used to skip this very short segments, but if
                you have a lot of them cumulatively, you can miss
                maxima or minima in the data. */
@@ -919,6 +948,8 @@ class PathSimplifier : protected EmbeddedQueue<9>
     bool m_moveto;
     bool m_after_moveto;
     bool m_clipped;
+    bool m_has_init;
+    double m_initX, m_initY;
     double m_lastx, m_lasty;
 
     double m_origdx;