Venison backstrap is one the best cuts to cook on a grill (whether it is a gas or charcoal grill).
Before the cooking process starts, make sure that the meat is completely thawed and at room temperature.
If you want to brine your meat, it can definitely be done with this recipe. Brine your meat for 24 hours in a salt and sugar mixture. This will add moisture and flavor to the meat.
Remember to remove the silver skin from the venison backstrap before cooking.