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Maximum clique problem is a classic problem in the domain of Social Network Analysis. It has always been concerned by people, and many algorithms have been proposed. However, most of the algorithms are based on single computer system. As the social network becoming more and more complex, the traditional analysis methods face significant challenges. This paper presents a distributed algorithm based on MapReduce, the algorithm can run parallelly in computer cluster, it is easy to implement, has good convergence rate and scalability. It works by expanding the current maximum clique step by step. Through the using of pruning optimization, we can reduce the solution space, and further improve the efficiency. This paper also gives testing results and shares some experience about dealing with such problems.