The Ethernet passive optical network is being regarded as the most promising for next-generation optical access solutions in the access networks. In time division multiplexing passive optical network technology (TDM-PON), the dynamic bandwidth allocation (DBA) plays a crucial key role to achieve efficient bandwidth allocation and fairness among subscribers. Therefore, the traffic prediction in DBA during the waiting time must be put into the account. In this paper, we propose a new prediction approach with an evolutionary algorithm Genetic Expression Programming (GEP) prediction incorporated with Limited IPACT referred as GLI-DBA to tackle the queue variation during waiting times as well as reducing the high priority packet delay. We setup the predictor in the GEP based on cycle time, waiting time, REPORT, GATE and history mean bandwidth request in every cycle time. Simulation results show that GEP prediction in DBA can reduce the EF packet delay, shorten the EF queue length, increase the Quality of Services (QoS) and maintain the fairness of ONUs. We conducted and evaluated detail simulation in three different traffic proportion scenarios. The results show that the GLI-DBA has EF end-to-end delay improvement up to 30% over dynamic bandwidth allocation for multiple of services (DBAM). It also shows that our proposed prediction scheme can improve IPACT and has better system performance than the DBAM in terms of system throughput and fairness.