This paper modifies the approach of scanning the transaction database of the Apriori algorithm for candidate itemsets, and adds the idea of the deleting the transaction data which do not contain the candidate itemsets. Two algorithms, called efficiency_Apriori and efficiency_MQA-1, are proposed to mine association rules and association rules including the quantities of items, respectively. The experiments show that the efficiency_Apriori algorithm and the efficiency_MQA-1 algorithm can effectively improve the performance of the Apriori algorithm and the MQA-1 algorithm, respectively.