Mining maximum frequent itemsets is a key problem in many data mining application. Most of the previous studies adopt an Apriori-like candidate set generation-and-test approach. However, candidate set generation is still costly, especially when there exist prolific patterns and/or long patterns. In this paper, a fast algorithm DMFIA (discover maximum frequent itemsets algorithm) and its updating algorithm UMFIA (update maximum frequent itemsets algorithm) based on frequent pattern tree (FP-tree) for mining maximum frequent itemsets is proposed. The algorithm UMFIA makes use of previous mining result to cut down the cost of finding new maximum frequent itemsets in an updated database.