In a stainless steel or glass bowl, combine garlic, olive oil, basil, salt, pepper, lemon juice, and parsley.
Place the halibut filets in a shallow glass dish or a resealable plastic bag, and pour the marinade over the fish. Cover or seal and place in the refrigerator for 1 hour, turning occasionally.
Preheat an outdoor grill for high heat and lightly oil grate. Set grate 4 inches from the heat.
Remove halibut filets from marinade and drain off the excess. Grill filets 5 minutes per side or until fish is done when easily flaked with a fork.