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In this paper, a suboptimal resource allocation algorithm is proposed with considered the long-term fairness in the downlink of the multiuser OFDM systems. The intention of this work is to minimize the total transmission power under the constraint of the target system data rate. After formulating the optimization problem, the subcarrier allocation algorithm, considered long-term rate fairness, is proposed with a water-filling bit assignment method. In order to guarantee the long-term fairness, the average date rate is introduced to weight the allocating factor in the process of the subcarrier allocation. Furthermore, the water-filling factor is also derived by a novel method in bit assignment procedure. In a conclusion, compared with the convention short term fairness algorithm, the proposed scheme not only guarantees the long term fairness, but also saves the power consumption obviously. The simulation results have shown the advanced performance of the proposed algorithm.