diff --git a/fsspec/asyn.py b/fsspec/asyn.py
index 5e9911535..b8f8642a0 100644
--- a/fsspec/asyn.py
+++ b/fsspec/asyn.py
@@ -641,7 +641,7 @@ async def _info(self, path, **kwargs):
     async def _ls(self, path, detail=True, **kwargs):
         raise NotImplementedError
 
-    async def _walk(self, path, maxdepth=None, **kwargs):
+    async def _walk(self, path, maxdepth=None, on_error="omit", **kwargs):
         if maxdepth is not None and maxdepth < 1:
             raise ValueError("maxdepth must be at least 1")
 
@@ -653,7 +653,11 @@ async def _walk(self, path, maxdepth=None, **kwargs):
         detail = kwargs.pop("detail", False)
         try:
             listing = await self._ls(path, detail=True, **kwargs)
-        except (FileNotFoundError, OSError):
+        except (FileNotFoundError, OSError) as e:
+            if on_error == "raise":
+                raise
+            elif callable(on_error):
+                on_error(e)
             if detail:
                 yield path, {}, {}
             else:
diff --git a/fsspec/spec.py b/fsspec/spec.py
index 2bdfa3854..457c082e2 100644
--- a/fsspec/spec.py
+++ b/fsspec/spec.py
@@ -372,7 +372,7 @@ def _ls_from_cache(self, path):
         except KeyError:
             pass
 
-    def walk(self, path, maxdepth=None, topdown=True, **kwargs):
+    def walk(self, path, maxdepth=None, topdown=True, on_error="omit", **kwargs):
         """Return all files belows path
 
         List all files, recursing into subdirectories; output is iterator-style,
@@ -399,6 +399,10 @@ def walk(self, path, maxdepth=None, topdown=True, **kwargs):
         topdown: bool (True)
             Whether to walk the directory tree from the top downwards or from
             the bottom upwards.
+        on_error: "omit", "raise", a collable
+            if omit (default), path with exception will simply be empty;
+            If raise, an underlying exception will be raised;
+            if callable, it will be called with a single OSError instance as argument
         kwargs: passed to ``ls``
         """
         if maxdepth is not None and maxdepth < 1:
@@ -412,7 +416,11 @@ def walk(self, path, maxdepth=None, topdown=True, **kwargs):
         detail = kwargs.pop("detail", False)
         try:
             listing = self.ls(path, detail=True, **kwargs)
-        except (FileNotFoundError, OSError):
+        except (FileNotFoundError, OSError) as e:
+            if on_error == "raise":
+                raise
+            elif callable(on_error):
+                on_error(e)
             if detail:
                 return path, {}, {}
             return path, [], []
diff --git a/fsspec/tests/test_api.py b/fsspec/tests/test_api.py
index 8187dda81..dd3374fe7 100644
--- a/fsspec/tests/test_api.py
+++ b/fsspec/tests/test_api.py
@@ -4,6 +4,7 @@
 import os
 import pickle
 import tempfile
+from unittest.mock import Mock
 
 import pytest
 
@@ -480,3 +481,18 @@ def _walk(*args, **kwargs):
         (dir12, [], ["file121"]),
         (dir1, ["dir11", "dir12"], ["file11"]),
     ]
+
+    # on_error omit by default
+    assert list(m.walk("do_not_exist")) == []
+    # on_error omit
+    assert list(m.walk("do_not_exist", on_error="omit")) == []
+    # on_error raise
+    with pytest.raises(FileNotFoundError):
+        list(m.walk("do_not_exist", on_error="raise"))
+    # on_error callable function
+    mock = Mock()
+    assert list(m.walk("do_not_exist", on_error=mock.onerror)) == []
+    mock.onerror.assert_called()
+    assert mock.onerror.call_args.kwargs == {}
+    assert len(mock.onerror.call_args.args) == 1
+    assert isinstance(mock.onerror.call_args.args[0], FileNotFoundError)