diff --git a/lib/src/legacy/importer.ts b/lib/src/legacy/importer.ts
index 09438e38..35e6f384 100644
--- a/lib/src/legacy/importer.ts
+++ b/lib/src/legacy/importer.ts
@@ -11,6 +11,7 @@ import * as util from 'util';
 import {resolvePath} from './resolve-path';
 import {
   fileUrlToPathCrossPlatform,
+  isErrnoException,
   thenOr,
   PromiseOr,
   SyncBoolean,
@@ -93,10 +94,29 @@ export class LegacyImporterWrapper<sync extends 'sync' | 'async'>
     // sure that all normal loads are preceded by exactly one relative load.
     if (this.expectingRelativeLoad) {
       if (url.startsWith('file:')) {
-        const resolved = resolvePath(
-          fileUrlToPathCrossPlatform(url),
-          options.fromImport
-        );
+        let resolved: string | null = null;
+
+        try {
+          const path = fileUrlToPathCrossPlatform(url);
+          resolved = resolvePath(path, options.fromImport);
+        } catch (error: unknown) {
+          if (
+            error instanceof TypeError &&
+            isErrnoException(error) &&
+            (error.code === 'ERR_INVALID_URL' ||
+              error.code === 'ERR_INVALID_FILE_URL_PATH')
+          ) {
+            // It's possible for `url` to represent an invalid path for the
+            // current platform. For example, `@import "/foo/bar/baz"` will
+            // resolve to `file:///foo/bar/baz` which is an invalid URL on
+            // Windows. In that case, we treat it as though the file doesn't
+            // exist so that the user's custom importer can still handle the
+            // URL.
+          } else {
+            throw error;
+          }
+        }
+
         if (resolved !== null) {
           this.prev.push({url: resolved, path: true});
           return pathToFileURL(resolved);
diff --git a/lib/src/utils.ts b/lib/src/utils.ts
index 7153faec..56c02dfa 100644
--- a/lib/src/utils.ts
+++ b/lib/src/utils.ts
@@ -133,6 +133,13 @@ export function protofySyntax(
   }
 }
 
+/** Returns whether `error` is a NodeJS-style exception with an error code. */
+export function isErrnoException(
+  error: unknown
+): error is NodeJS.ErrnoException {
+  return error instanceof Error && ('errno' in error || 'code' in error);
+}
+
 /**
  * Dart-style utility. See
  * http://go/dart-api/stable/2.8.4/dart-core/Map/putIfAbsent.html.