Aiming at the redundancy problem of association rules in the mining process of mining association rules, a kind of shortest antecedent set algorithm (SASA) for mining association rules is proposed in this paper, and the algorithm is supported by the set-enumeration tree structure. The proposed algorithm is able to record a kind of subset for association rules without any information loss, and this kind of subset contains the entire generated association rule nondestructive. Experimental results show that the algorithm can significantly reduce the number of association rules, and it also improves the efficiency of analyzing the association rules for users.