Combine sugar, vinegar and salt in a large saucepan; bring to a boil, stirring to dissolve sugar.
Add grapes, onion, ginger, mustard seeds, cinnamon, and crushed red pepper. Return to a boil. Reduce heat; simmer 20 minutes. Press grapes against side of pan to release juices.
Cook, stirring often, until little liquid remains, 35 to 40 minutes. Cool completely. Use in sandwiches, with grilled meats or on a cheese board. Store in the refrigerator up to 2 weeks.