This paper provides a heuristic algorithm for an NP-Complete problem. It is a result of a research on an NP-Complete problem known as Clique problem. I have succeeded in developing an algorithm which will give the maximum size Clique, for a given graph G, as its output. This paper explains the algorithm, its time complexity, applications and its implementation in C. This is a research paper based on an interesting class of problems known as ?NP-Complete? problems. No polynomial-time algorithm has yet been discovered for an NP-Complete problem, nor has any one yet been able to prove a superpolynomial-time lower bound for any of them. This so called whether P ? NP question has been one of the deepest, most perplexing open research problems in theoretical Computer Science since it was posed in 1971.