This paper integrates the advantage of the FP-Tree algorithm for mining association rules and the maximum clique theory of graph. The main contributions include: (1) An improved method to mine frequent 2-itemset by adjacency matrix is proposed. (2) The concept of maximum ordered frequent itemset is proposed, and the equivalence of Head Relation is proved as along with the theorems about Local Complexity and Merge Convergence Range. (3) The MaxCFPTree algorithm based on Maximum-clique partition is proposed and implemented with complexity O(n²). (4) The algorithms are validated by extensive experiments. The conflict between memory and huge number of items is resolved, and the system efficiency and scalability are improved.