diff --git a/Lib/test/test_zipfile/test_core.py b/Lib/test/test_zipfile/test_core.py
index ffed328b171fda2..f51093a52eda16d 100644
--- a/Lib/test/test_zipfile/test_core.py
+++ b/Lib/test/test_zipfile/test_core.py
@@ -2711,6 +2711,16 @@ def test_overlap_with_archive_comment(self):
             with self.assertRaisesRegex(zipfile.BadZipFile, 'Overlapped entries'):
                 zipf.read('a')
 
+    def test_reading_archive_member_starts_with_slash(self):
+        member_path = '/folder/file.txt'
+        member_data = b'hello world'
+        with open(TESTFN, "wb") as f:
+            f.write(member_data)
+        with zipfile.ZipFile(TESTFN2, 'w') as zf:
+            zf.write(TESTFN, member_path)
+        with zipfile.ZipFile(TESTFN2) as zf:
+            self.assertEqual(zf.read(member_path), member_data)
+
     def tearDown(self):
         unlink(TESTFN)
         unlink(TESTFN2)
diff --git a/Lib/zipfile/__init__.py b/Lib/zipfile/__init__.py
index 005b6f4eb840448..47b548a41d38a42 100644
--- a/Lib/zipfile/__init__.py
+++ b/Lib/zipfile/__init__.py
@@ -644,7 +644,10 @@ def from_file(cls, filename, arcname=None, *, strict_timestamps=True):
         if arcname is None:
             arcname = filename
         arcname = os.path.normpath(os.path.splitdrive(arcname)[1])
-        while arcname[0] in (os.sep, os.altsep):
+        while (arcname[0] in (os.sep, os.altsep) and
+               arcname[1] in (os.sep, os.altsep)):
+            arcname = arcname[1:]
+        if arcname[0] in (os.sep, os.altsep) and os.sep not in arcname[1:]:
             arcname = arcname[1:]
         if isdir:
             arcname += '/'
diff --git a/Misc/NEWS.d/next/Library/2020-10-22-07-07-17.bpo-42112.Z_ED9N.rst b/Misc/NEWS.d/next/Library/2020-10-22-07-07-17.bpo-42112.Z_ED9N.rst
new file mode 100644
index 000000000000000..fdda11afbbb884e
--- /dev/null
+++ b/Misc/NEWS.d/next/Library/2020-10-22-07-07-17.bpo-42112.Z_ED9N.rst
@@ -0,0 +1,2 @@
+Fix unnecessary removing of a leading slash in :meth:`zipfile.ZipInfo.from_file`
+when member's archive name is in the form of :code:`/directory/filename`.