diff --git a/Lib/pathlib.py b/Lib/pathlib.py
index 37934c6038e1d1..1cb29a7d325110 100644
--- a/Lib/pathlib.py
+++ b/Lib/pathlib.py
@@ -15,7 +15,7 @@
 
 
 if os.name == 'nt':
-    from nt import _getfinalpathname
+    from nt import _getfinalpathname, _getfullpathname
 else:
     _getfinalpathname = None
 
@@ -189,26 +189,26 @@ def compile_pattern(self, pattern):
     def resolve(self, path, strict=False):
         s = str(path)
         if not s:
-            return path._accessor.getcwd()
+            s = path._accessor.getcwd()
+        if _getfinalpathname is None:
+            return None  # Means fallback on absolute
+        if strict:
+            return self._ext_to_normal(_getfinalpathname(s))
+        s = path = _getfullpathname(s)
         previous_s = None
-        if _getfinalpathname is not None:
-            if strict:
-                return self._ext_to_normal(_getfinalpathname(s))
+        tail_parts = []  # End of the path after the first one not found
+        while True:
+            try:
+                s = self._ext_to_normal(_getfinalpathname(s))
+            except FileNotFoundError:
+                previous_s = s
+                s, tail = os.path.split(s)
+                tail_parts.append(tail)
+                if previous_s == s:
+                    # Root reached, fallback to _getfullpathname()
+                    return path
             else:
-                tail_parts = []  # End of the path after the first one not found
-                while True:
-                    try:
-                        s = self._ext_to_normal(_getfinalpathname(s))
-                    except FileNotFoundError:
-                        previous_s = s
-                        s, tail = os.path.split(s)
-                        tail_parts.append(tail)
-                        if previous_s == s:
-                            return path
-                    else:
-                        return os.path.join(s, *reversed(tail_parts))
-        # Means fallback on absolute
-        return None
+                return os.path.join(s, *reversed(tail_parts))
 
     def _split_extended_path(self, s, ext_prefix=ext_namespace_prefix):
         prefix = ''
diff --git a/Lib/test/test_pathlib.py b/Lib/test/test_pathlib.py
index 6ed08f7e70ce3d..4fbd46f4923c88 100644
--- a/Lib/test/test_pathlib.py
+++ b/Lib/test/test_pathlib.py
@@ -1799,6 +1799,16 @@ def test_resolve_dot(self):
         # Non-strict
         self.assertEqual(r.resolve(strict=False), p / '3' / '4')
 
+    def test_resolve_nonexist_relative_issue38671(self):
+        p = self.cls('non', 'exist')
+
+        old_cwd = os.getcwd()
+        os.chdir(BASE)
+        try:
+            self.assertEqual(p.resolve(), self.cls(BASE, p))
+        finally:
+            os.chdir(old_cwd)
+
     def test_with(self):
         p = self.cls(BASE)
         it = p.iterdir()
diff --git a/Misc/NEWS.d/next/Library/2019-12-28-02-50-12.bpo-38671.xT4R0P.rst b/Misc/NEWS.d/next/Library/2019-12-28-02-50-12.bpo-38671.xT4R0P.rst
new file mode 100644
index 00000000000000..a012fa57c3d976
--- /dev/null
+++ b/Misc/NEWS.d/next/Library/2019-12-28-02-50-12.bpo-38671.xT4R0P.rst
@@ -0,0 +1,2 @@
+Ensure pathlib.Path.resolve(strict=False) returns an absolute path on
+Windows when the path is relative and does not exist.