Most of multidimensional association rule mining algorithms such as mining algorithms based on data cube assume that an object attribute only has a single-value. In this paper, the attribute value of an object is extended to a multi-value and the concept of multidimensional set is presented, which brings about the semantics of multidimensional set association rule. Based on the semantics, an algorithm to mine association rules of multidimensional sets is given. The algorithm makes use of the restricted characteristics of multidimensional set association rule and can execute a triplicate pruning of candidate sets with a reduction of data set, which makes it a better performance than that of apriori and other algorithms. The performance, correctness and completeness of the algorithm are analyzed, and its effectiveness is also proved by experiments.