The Ethernet Passive Optical Network (EPON) combines both the inexpensive Ethernet equipments and the large-bandwidth offered by the optical fiber. Therefore, EPON has been considered as an attractive solution for the next generation broadband access network. In this paper, we present an enhanced Dynamic Bandwidth Allocation (eDBA) algorithm for EPON networks. Our mechanism allocates effectively and fairly the transmission bandwidth to the end-users. Some other algorithms, such as the Dynamic Bandwidth Allocation (DBA), introduce an idle period during the time that the Optical Line Terminal (OLT) is executing the bandwidth assignment procedure. During this idle time, no data are sent by any node to the OLT. In order to exploit this wasted bandwidth, the proposed algorithm calculates a vector of complementary bandwidth amounts to assign to the end users during the idle time. Finally, we simulate the studied EPON multiservice network configured with the eDBA mechanism. Obtained results are compared to the ones obtained with two other algorithms: Dynamic Bandwidth Allocation (DBA) and the Interleaved Polling with Adaptive Cycle Time (IPACT). We show that eDBA can significantly improve the network performance in term of packet access delay and packet loss rate as compared with other algorithms