The ideal time to cook a filet mignon steak depends on the thickness of the steak and the desired level of doneness, according to Better Homes and Gardens. A 1-inch steak needs to grill for 10 to 12 minutes to reach 145 degrees Fahrenheit, which is medium rare.
The same steak takes roughly 12 to 15 minutes to reach medium, which is 160 degrees. A thicker 1.5-inch cut needs 15 to 19 minutes to reach medium rare or 18 to 23 minutes to reach medium. Once the meat is cooked through, it should be removed from heat and left to stand for 5 minutes before serving. A grill should always be preheated before using it to cook steak.