Frequent Itemset Mining (FIM) is one of the most investigated fields of data mining. The goal of Frequent Itemset Mining (FIM) is to find the most frequently-occurring subsets from the transactions within a database. Many methods have been proposed to solve this problem, and the Apriori algorithm is one of the best known methods for frequent Itemset mining (FIM) in a transactional database. In this paper, a parallel Frequent Itemset Mining Algorithm, called Accelerating Parallel Frequent Itemset Mining on Graphic Processors with Sorting (APFMS), is presented. This algorithm utilizes new-generation graphic processing units (GPUs) to accelerate the mining process. In it, massive processing units of GPU were used to speed up the frequent item verification procedure on the OpenCL platform. The experimental results demonstrated that the proposed algorithm had dramatically reduced computation time compared with previous methods.