To grill filet mignon on a gas grill:

• For a 1-inch thick filet mignon, grill at 450°F about 10–11 minutes total to reach medium-rare (130°–135°F). This usually involves grilling 4–5 minutes per side and then monitoring internal temperature to prevent overcooking.
• Thicker filets (about 1½ inches) will take a few minutes longer, around 12-14 minutes for medium, with searing 2-3 minutes per side on high heat, then finishing on medium-low heat.
• General estimated times on a 450°F grill are:
  • Rare: 6–8 minutes total,
  • Medium-rare: 10–11 minutes,
  • Medium: 12–14 minutes,
  • Medium-well: 14–16 minutes,
  • Well-done (not recommended): 16+ minutes.
• Using a meat thermometer is highly recommended—remove the steak 3–5 degrees before the target temperature to allow for carryover cooking during resting.
• Let the filet rest for 5-10 minutes after grilling to redistribute juices.

In summary, about 10-12 minutes total for a 1-inch filet mignon to medium-rare on a well-heated grill is typical, with adjustments for thickness and doneness preference. Always check internal temperature for best results.