How to Grill Filet Mignon. 1  For a charcoal grill, place the meat on a grill rack directly over medium coals; grill uncovered. 2  For a gas grill, preheat the grill; reduce the heat to medium. 3  Place the filet on the grill rack over the heat. 4  Cover the grill. Place the filet on the grill rack over the heat. 2  Cover the grill. 3  Use the following timings for grilling filet mignon, and turn once halfway through the grilling time: 4  For a 1-inch cut, grill 10 to 12 minutes for medium rare (145 degrees F) or 12 to 15 minutes for medium (160 degrees F).