A broadband access network is required for supporting the increased Internet data traffic. One of the most cost-effective solutions is the Ethernet Passive Optical Networks (E-PONs) with the efficient bandwidth assignment function by which the upstream bandwidth can be shared among access users. To satisfy the services with heterogeneous QoS characteristics, it is very important to provide QoS guaranteed network access while utilize the bandwidth efficiently. In this paper, a dual DEB-GPS scheduler in E-PON is presented to provide delay-constraint and lossless QoS guarantee to QoS service and maximize the bandwidth to best-effort service. Simulation results show our scheme outperforms the conventional bandwidth allocation scheme in EPON system.