Preheat grill to 350° to 400° (medium-high) heat. Stir together first 6 ingredients. Brush turkey tenderloin with olive oil, and rub with brown sugar mixture.
Grill turkey, covered with grill lid, over 350° to 400° (medium-high) heat 10 minutes on each side or until a meat thermometer inserted into thickest portion registers 165°. Let stand 10 minutes before serving.