Algorithms for mining association rules based on the Apriori algorithm use the hash tree data structure for storing and counting supports of the candidate frequent itemsets and the most part of the execution time is consumed for searching in the hash tree. The DHP(Direct Hashing and Pruning) algorithm makes efforts to reduce the number of the candidate frequent itemsets to save searching time in the hash tree. For this purpose, the DHP algorithm does preparative simple counting supports of the candidate frequent itemsets. At this time, the DHP algorithm uses the direct hash table to reduce the overhead of the preparative counting supports. This paper proposes and evaluates an efficient hashing mechanism for the direct hash table $H_2$ which is for pruning in phase 2 and the hash tree $C_k$, which is for counting supports of the candidate frequent itemsets in all phases. The results showed that the performance improvement due to the proposed hashing mechanism was 82.2% on the maximum and 18.5% on the average compared to the conventional method using a simple mod operation.