Preheat the gas grill to high heat, about 450–500°F
Clean and oil the grill grates
Pat the filet mignon dry with paper towels
Season both sides with salt and black pepper
Brush lightly with oil if desired
Place the filet mignon on the hottest part of the grill
Grill for 4–5 minutes without moving it
Flip the steak once
Grill the second side for 3–5 minutes for medium-rare, or longer for desired doneness
Use a meat thermometer to check internal temperature
Remove at 125°F for rare, 130–135°F for medium-rare, 140–145°F for medium
Transfer the steak to a plate or cutting board
Let it rest for 5–10 minutes
Slice and serve