Place tuna steaks in a large heavy-duty zip-top plastic bag.
Combine olive oil and next 6 ingredients in a small bowl: stir well.
Pour marinade mixture over steaks. Seal bag securely; place in a large bowl.
Marinate in refrigerator for 30 minutes.
Remove steaks from marinade.
Spray a grill with cooking spray, and place steaks on grill.
Cook steaks, covered, over medium coals, basting frequently, for 6 minutes on each side or until fish flakes easily when tested with a fork.