A new algorithm based on an FC-tree (frequent closed pattern tree) and a max-FCIA (maximal frequent closed itemsets algorithm) is presented, which is used to mine the frequent closed itemsets for solving memory and time consuming problems. This algorithm maps the transaction database by using a Hash table,gets the support of all frequent itemsets through operating the Hash table and forms a lexicographic subset tree including the frequent itemsets.Efficient pruning methods are used to get the FC-tree including all the minimum frequent closed itemsets through processing the lexicographic subset tree.Finally,frequent closed itemsets are generated from minimum frequent closed itemsets.The experimental results show that the mapping transaction database is introduced in the algorithm to reduce time consumption and to improve the efficiency of the program.Furthermore,the effective pruning strategy restrains the number of candidates,which saves space.The results show that the algorithm is effective.