Even if your child will not willingly take a nap, it's important to have "quiet time". He can stay in his room with a pile of books, or a story CD, or soft music, and relax in bed. Sometimes kids will fall asleep when distracted. Either way, it will give his body some time to relax, which is important.

Somewhere between 3 and 4 years of age, children begin to give up naps.  That is a normal part of growing up; however, even though your child may not want to nap, he still needs to rest during the day.  You can help him recharge his energy by starting a daily ritual of a quiet time after lunch.  To help him understand the length of the quiet time, set a timer, and let him know that his activity will end when the timer goes off.  

Best regards.