diff --git a/src/path.cpp b/src/path.cpp
index 2cfcb80c6..d5ab52c66 100644
--- a/src/path.cpp
+++ b/src/path.cpp
@@ -179,9 +179,14 @@ maybe_t<wcstring> path_get_cdpath(const wcstring &dir, const wcstring &wd,
             if (next_path.empty()) next_path = L".";
             if (next_path == L"." && !wd.empty()) {
                 // next_path is just '.', and we have a working directory, so use the wd instead.
-                // TODO: if next_path starts with ./ we need to replace the . with the wd.
                 next_path = wd;
             }
+
+            // If next_path starts with ./ we need to replace the . with the wd.
+            if (string_prefixes_string(L"./", next_path) && !wd.empty()) {
+                next_path = next_path.replace(0, 2, wd);
+            }
+
             expand_tilde(next_path, env_vars);
             if (next_path.empty()) continue;
 
diff --git a/tests/cd.in b/tests/cd.in
index e70a7f902..88718c16a 100644
--- a/tests/cd.in
+++ b/tests/cd.in
@@ -72,6 +72,9 @@ cd $base
 test $PWD = $base; and echo Gone to base
 cd linkhome
 test $PWD = $base/linkhome; and echo Gone to linkhome via implicit . in CDPATH
+set -g CDPATH ./
+cd $base
+test $PWD = $base; and echo No crash with ./ CDPATH
 
 # cd back before removing the test directory again.
 cd $oldpwd
diff --git a/tests/cd.out b/tests/cd.out
index d3801a10a..8c786556a 100644
--- a/tests/cd.out
+++ b/tests/cd.out
@@ -29,3 +29,4 @@ BogusPWD test 2 succeeded
 Gone to linkhome via CDPATH
 Gone to base
 Gone to linkhome via implicit . in CDPATH
+No crash with ./ CDPATH