how long to cook filet on gas grill
1 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).