Set all the burners of a gas grill to high heat and allow to preheat for at least 5 minutes. Clean and oil the grilling grate.
Pat dry calamari tubes with paper towels and season them with olive oil until lightly coated.
Grill calamari tubes over hottest part of grill, until browned on both sides, about 5-6 minutes.
Transfer to a platter and season with salt and pepper. Drizzle with more olive oil, garnish with parsley and serve with lemon wedges.