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Maximal frequent itemsets are one of several condensed representations of frequent itemsets, which store most of the information contained in frequent itemsets using less space, thus being more suitable for stream mining. This paper considers a problem that to the best of our knowledge has not been addressed, namely, how to use GPU to mine maximal frequent itemsets in an incremental fashion. Our method employs a single-instruction-multiple-data architecture to accelerate the mining speed with using a bitmap data representation of frequent itemsets; moreover, we use an inverse tree structure to prune efficiently. Our experimental results show that our algorithm achieves a better performance in running time.