Gigabit passive optical network (GPON) and Long Term Evolution (LTE) are two promising broadband access technologies for next-generation fiber-wireless network. With the advantage of their complementary features can be used to make up each other’s drawbacks, optical part can be unrestricted from the geography and wireless part can have higher transfer rate, we propose an integrated architecture to converge GPON and LTE. Based on this architecture, a hierarchical dynamic bandwidth assignment with admission control is proposed to well transmit heterogeneous traffic in this paper. First, we combine the ONU with evolve node B into an ONU-eNB device and briefly describe each function module. Second, a dynamic delay-based call admission control scheme is proposed to guarantee the required QoS for each request to maximize the throughput. Third, we propose two steps hierarchical DBA that first layer optical line terminal allocates the bandwidth and the second layer bandwidth reassignment will be executed followed by service level agreement in ONU-eNB. Simulation results show that the proposed scheme can improve the throughput about 3–10 % and increase about 60–210 requests for users while the QoS is met.