Ethernet passive optical network (EPON) is one of the energy-efficient access networks. Many studies have been done to reach maximum energy saving in the EPON. However, it is a trade-off between achieving maximum energy saving and guaranteeing QoS. In this paper, a predictive doze mode mechanism in an enhanced EPON architecture is proposed to achieve energy saving by using a logistic regression (LR) model. The optical line terminal (OLT) in the EPON employs an enhanced Doze Manager practicing the LR model to predict the doze periods of the optical network units (ONUs). The doze periods are estimated more accurately based on the historical high-priority traffic information, and logistic regression DBA (LR-DBA) performs dynamic bandwidth allocation accordingly. The proposed LR-DBA mechanism is compared with a scheme without energy saving (IPACT) and another scheme with energy saving (GDBA). Simulation results show that LR-DBA effectively improves the power consumption of ONUs in most cases, and the improvement can be up to 45% while it guarantees the QoS metrics, such as the high-priority traffic delay and jitter.