Association rule mining is an important data mining problem that has been studied extensively. In this paper, a simple but Fast algorithm for Intersecting attribute lists using a hash Table (FIT) is presented. FIT is designed for efficiently computing all the frequent itemsets in large databases. It deploys the similar idea as Eclat but has a much better computation performance than Eclat due to two aspects: 1) FIT has fewer total number of comparisons for each intersection operation between two attribute lists, 2) FIT significantly reduces the total number of intersection operations. The experimental results demonstrate that the performances of FIT are much better than those of Eclat and Apriori algorithms.