Aiming at the problems that in the big data environment, the Can-tree based incremental association rule algorithm had problems such as too much space occupation of the tree structure, inability to dynamically set the support threshold, and too much time consumption during the data transfer process between the Map and Reduce stages, the Map Reduce-based parallel association rules incremental mining algorithm using information entropy and genetic algorithm (MR-PARIMIEG)was proposed.Firstly, a similar items merging based on information entropy (SIM-IE) was designed to merge similar data items, and a Can tree based on the merged data set was constructed, thereby reducing the space occupation of the tree structure.Secondly, the dynamic support threshold obtaining using genetic algorithm (DST-GA) was proposed to obtain the relatively optimal dynamic support threshold in the big data environment, and frequent itemset mining was performed according to this threshold to avoid the unnecessary time consumption caused by mining redundant frequent patterns.Finally, in the process of MapReduce parallel operation, the parallel LZO data compression algorithm was used to compress the output data of the Map stage, thereby reducing the size of the transmitted data, and finally improving the running speed of the algorithm.Experimental simulation results show that MR-PARIMIEG has better performance when mining frequent item sets in the big data environment, and it is suitable for parallel processing of larger data sets.