In a large resealable plastic bag, combine the teriyaki sauce, oil, garlic, and pepper. Place the tuna fillets in the bag. Seal the bag with as little air in it as possible. Give the mix a good shake, to ensure the tuna fillets are well coated. Marinate for 30 minutes in the refrigerator.
Meanwhile, preheat an outdoor grill for high heat, and lightly oil grate.
Remove tuna from marinade, and place on grill. For rare tuna, grill for 3 to 5 minutes on each side. For medium, grill 5 to 8 minutes per side. For well done, grill for 8 to 10 minutes per side.