In a small bowl stir together the mayonnaise, vinegar, sugar, mustard, salt, and pepper.
In a large bowl combine the cabbage, apples, pickles, grapes, and onion. Add the mayonnaise mixture to the cabbage mixture; toss to coat. Cover and chill in the refrigerator for 2 to 6 hours before serving. Stir before serving. Makes 6 to 8 servings.