In theory if it never gets connected to the Internet and you never transfer any files to it in any way, then no you wouldn't need AV.
But in reality, very very few people use a computer of any sort so it's totally isolated from all external influences, then yes you do need AV.
You need decent anti-virus as a must, wise extras are a decent antimalware program as well.
Anti-virus (Microsoft security essentials)
http://www.google.com...MSE&ie=utf-8&oe=utf-8
Anti-malware (malwarebytes)
http://www.google.com...dx5o2D8ZtHdZVy_7xNQEw
If you are really concerned about security then buy a decent all in one security package rather than using free stuff (you can do the same with free, but the effort isn't worth the £20 a year it's going to cost)