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Ethernet passive optical access network (EPON) combined with IP transportation and PON transparent broadband transmission is considered a major means for broadband access and FTTH in the future. It has advantages of low-cost, compatibility, simplicity, flexibility, and so on. How to maximize the utilization of limited bandwidth of upstream bandwidth among optical network units (ONUs) is one of the key issues in EPON system. This paper proposes a new concentrated bandwidth allocation algorithm of lightly-loaded-ONU-first and heavily-loaded-ONU-twice-assigned. By adjusting ONUs' scheduling, this algorithm improves the implementation of EPON. Simulation results show that this algorithm outperforms the existing algorithms in overhead bandwidth loss, average packet delay, and average queue length.