In a large resealable plastic bag, combine the teriyaki sauce, oil, garlic and pepper. Place the tuna in the bag. Seal the bag with as little air in it as possible. Give the bag a good shake to coat the tuna fillets. Marinate for 30 minutes in the refrigerator.
Meanwhile, preheat the barbecue for high heat and lightly oil cooking grill hotplate.
Remove tuna from marinade, and place on barbecue. Cook for about 10 minutes or to desired doneness.