Yes absolutely. A 20 Gauge is more than enough gun for a deer, or most large game within it's effective range. Black bear are highly over rated as far as how tough they are to kill. If you have ever skinned one out, you'll notice that their hide is not as thick as a Whitetail deer's hide, and in my opinion, most mature bucks are far harder to kill than any Black bear that I have ever shot. Shoot a good quality slug like Federal or Winchester or what ever your gun prefers and shoots well, and you shoudn't have any problem at all. Especially if you are hunting over bait!