Mix the olive oil, garlic, lemon juice, and parsley in a small bowl.
Place the salmon in a 9x13-inch casserole dish or a large mixing bowl and pour over the marinade. Flip the salmon several times to coat salmon flesh side evenly. Cover the casserole dish with plastic wrap and place it in the refrigerator for 1 hour.
Pat the salmon dry with paper towels. Discard the remaining marinade.
Preheat your grill for five minutes. Brush a bit of oil on the grill grates. Season just before grilling with salt and pepper. Cook the salmon skin side down for four minutes, then flip and cook the flesh side for another four minutes, or until salmon turns a vibrant orange-red color through the center, with an internal temperature of 120 degrees Fahrenheit for medium-rare and 125 degrees Fahrenheit for medium.
Remove the salmon from the grill, garnish with additional fresh herbs and lemon wedges if desired, and serve right away.