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To increase the efficiency of data mining is the research emphasis in this field at present. Through the establishment of transaction-item association matrix, this paper changes the process of association rule mining to elementary matrix operation, which makes the process of data mining clear and simple. Compared with algorithms like Apriori, this method avoids the demerit of traversing the database repetitiously, and increases the efficiency of association rule mining obviously in the use of sparse storage technique for large-scale matrix. To incremental type of transaction matrix, it can also make the maintainment of association rule more convenient in the use of partitioning calculation technique of matrix. The transaction-item association matrix proposed in this paper can be seemed as the mathematical foundation of association rule mining algorithm.