Place the barramundi fillets on a large plate, and brush to coat them evenly with olive oil.
Mix the remaining ingredients together in a small bowl or bag, and sprinkle over the olive oil-coated fish fillets.
Place the fish fillets on the grill, skin-side down.
Close the grill top, and turn the heat down to medium, 325 F.
Allow the fillets to cook for 7 ½ minutes, then open the grill top, and carefully work a heat-proof spatula under the fish to help it release from the grill grates.
Flip the fish over and cook for another 7 ½ minutes.
Carefully work your heat-proof spatula under the fish once more, and remove both fillets from the grill.