In this paper, the new scheduling algorithm that supports the maximization of system throughput and the proportional fairness among non-real time traffic users is proposed in OFDMA wireless mobile communication systems. The concept of the proposed algorithm is based on the proportional fairness algorithm, which is deployed in 3GPP2, and sorting method. The proportional fairness algorithm is adapted to allocate the number of subcarrier per user. A sorting method is contributed to the maximization of system throughput in the practical allocation of subcarrier per user. Simulation results show that new algorithm had better performance than the max rate rule in case of fairness, higher throughput than the scheduling algorithm without sorting method. Even though the system throughput of the proposed algorithm is almost same with the iteration scheme using subcarrier swapping method between users, the computational time of the former is reduced up to 3 times than the latter.