I've gone through much of the detail on how to properly grill a backstrap of venison (or elk, antelope, bison, moose etc.) above, but remember that this is done over high heat with the grill top open, and that it takes a good 15 to 20 minutes. Be patient and you will be rewarded.
Coat the venison backstrap in oil and salt well. Set aside for 30 minutes to 1 hour at room temperature.
Get your grill hot, clean the grates and lay the venison on the grill. Keep the grill cover open. Let this cook 5 to 7 minutes without moving, depending on how hot your grill is and how thick your venison loin is. You want a good sear, with good grill marks, on that side of the meat. Flip and repeat on the other side.
Do the finger test to check for doneness. If the venison needs some more time, turn it to sides that have not had direct exposure to the grill and cook for 2 to 3 more minutes, checking all the way. If you are using a barbecue sauce, paint the meat with it and let it caramelize on the meat for a minute or three.
When the meat has been cooked to your liking, take it off the fire and let it rest for 5 to 10 minutes. If you are using a spice rub now is the time to roll the meat in it.
Notes
If you use a sauce with this recipe, serve the venison with a side salad like potato, macaroni or bean salad, plus maybe some tomatoes and basil, corn on the cob, dinner rolls --- you get the idea. Nothing overly fancy.
Keys to Success
If you want to use a marinade, I have lots of potential venison marinades here. You can marinate a venison steak up to a day in advance.
Let the venison come to room temperature. It will help it cook more evenly. Salting it when it comes out of the fridge helps season the steak better, too.
All meats taste best grilled over wood. Charcoal is good, too, but gas isn't. If that's what you have, soak some wood chips in water for an hour or two and burn them as you grill. The smoke will help flavor the meat.
Leftover grilled venison, if there is any, is good for sandwiches the next day.