diff --git a/Lib/test/test_mmap.py b/Lib/test/test_mmap.py
index 08b0714da02..8f20d969661 100644
--- a/Lib/test/test_mmap.py
+++ b/Lib/test/test_mmap.py
@@ -334,6 +334,19 @@ class MmapTests(unittest.TestCase):
             with mmap.mmap(f.fileno(), 0, offset=65536, access=mmap.ACCESS_READ) as mf:
                 self.assertRaises(IndexError, mf.__getitem__, 80000)
 
+    def test_length_0_large_offset(self):
+        # Issue #10959: test mapping of a file by passing 0 for
+        # map length with a large offset doesn't cause a segfault.
+        if not hasattr(os, "stat"):
+            self.skipTest("needs os.stat")
+
+        with open(TESTFN, "wb") as f:
+            f.write(115699 * b'm') # Arbitrary character
+
+        with open(TESTFN, "w+b") as f:
+            self.assertRaises(ValueError, mmap.mmap, f.fileno(), 0,
+                              offset=2147418112)
+
     def test_move(self):
         # make move works everywhere (64-bit format problem earlier)
         f = open(TESTFN, 'wb+')
diff --git a/Misc/NEWS b/Misc/NEWS
index 03912b3cff1..44d39cf71d1 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -16,6 +16,9 @@ Core and Builtins
 Library
 -------
 
+- Issue #10955: Fix a potential crash when trying to mmap() a file past its
+  length.  Initial patch by Ross Lagerwall.
+
 - Issue #10898: Allow compiling the posix module when the C library defines
   a symbol named FSTAT.
 
diff --git a/Modules/mmapmodule.c b/Modules/mmapmodule.c
index f3b2f503dfd..a9049ed1cf9 100644
--- a/Modules/mmapmodule.c
+++ b/Modules/mmapmodule.c
@@ -1116,6 +1116,11 @@ new_mmap_object(PyTypeObject *type, PyObject *args, PyObject *kwdict)
 #  endif
     if (fd != -1 && fstat(fd, &st) == 0 && S_ISREG(st.st_mode)) {
         if (map_size == 0) {
+            if (offset >= st.st_size) {
+                PyErr_SetString(PyExc_ValueError,
+                                "mmap offset is greater than file size");
+                return NULL;
+            }
             map_size = st.st_size - offset;
         } else if ((size_t)offset + (size_t)map_size > st.st_size) {
             PyErr_SetString(PyExc_ValueError,
@@ -1300,6 +1305,12 @@ new_mmap_object(PyTypeObject *type, PyObject *args, PyObject *kwdict)
             else
                 m_obj->size = low;
 #endif
+            if (offset >= m_obj->size) {
+                PyErr_SetString(PyExc_ValueError,
+                                "mmap offset is greater than file size");
+                Py_DECREF(m_obj);
+                return NULL;
+            }
             m_obj->size -= offset;
         } else {
             m_obj->size = map_size;