diff --git a/pylsp/plugins/jedi_completion.py b/pylsp/plugins/jedi_completion.py
index 4c4bc94e..90b4c191 100644
--- a/pylsp/plugins/jedi_completion.py
+++ b/pylsp/plugins/jedi_completion.py
@@ -2,7 +2,7 @@
 # Copyright 2021- Python Language Server Contributors.
 
 import logging
-import os.path as osp
+import os
 
 import parso
 
@@ -219,10 +219,20 @@ def _format_completion(d, markup_kind: str, include_params=True, resolve=False,
     if resolve:
         completion = _resolve_completion(completion, d, markup_kind)
 
+    # Adjustments for file completions
     if d.type == 'path':
-        path = osp.normpath(d.name)
+        path = os.path.normpath(d.name)
         path = path.replace('\\', '\\\\')
         path = path.replace('/', '\\/')
+
+        # If the completion ends with os.sep, it means it's a directory. So we add an escaped os.sep
+        # at the end to ease additional file completions.
+        if d.name.endswith(os.sep):
+            if os.name == 'nt':
+                path = path + '\\\\'
+            else:
+                path = path + '\\/'
+
         completion['insertText'] = path
 
     if include_params and not is_exception_class(d.name):
diff --git a/test/plugins/test_completion.py b/test/plugins/test_completion.py
index 16e278e0..fc22c34f 100644
--- a/test/plugins/test_completion.py
+++ b/test/plugins/test_completion.py
@@ -528,3 +528,26 @@ def foo():
     com_position = {'line': 1, 'character': 10}
     completions = pylsp_jedi_completions(doc._config, doc, com_position)
     assert completions[0]['label'] == 'foo()'
+
+
+def test_file_completions(workspace, tmpdir):
+    # Create directory and a file to get completions for them.
+    # Note: `tmpdir`` is the root dir of the `workspace` fixture. That's why we use
+    # it here.
+    tmpdir.mkdir('bar')
+    file = tmpdir.join('foo.txt')
+    file.write('baz')
+
+    # Content of doc to test completion
+    doc_content = '"'
+    doc = Document(DOC_URI, workspace, doc_content)
+
+    # Request for completions
+    com_position = {'line': 0, 'character': 1}
+    completions = pylsp_jedi_completions(doc._config, doc, com_position)
+
+    # Check completions
+    assert len(completions) == 2
+    assert [c['kind'] == lsp.CompletionItemKind.File for c in completions]
+    assert completions[0]['insertText'] == ('bar' + '\\\\') if os.name == 'nt' else ('bar' + '\\/')
+    assert completions[1]['insertText'] == 'foo.txt"'