This project investigates modelling and control approaches to optimize the efficiency and power factor for discontinuous conduction mode (DCM) boost power factor correction (PFC) converters. First, with detailed consideration of parasitic and GaN HEMT transients, the input and output charges of the converter are exactly derived, where the rate forms the comprehensive charge rate (CCR) model. Second, based on the CCR model, the overall efficiency is derived. Since the overall efficiency is only related to the input voltage, output voltage and switching on-time, an optimal on-time is calculated to achieve the maximum efficiency. Furthermore, with the optimal on-time, a maximum efficiency average current (MEAC) controller is proposed to regulate the input current, while maintaining the maximum efficiency. With the pre-defined optimal on-time, a switching cycle modulation method is adopted to regulate the input current as sinusoid, which improves the power factor to unity. Finally, effectiveness of the MEAC control strategy is verified by simulations and experiments. Compared with conventional constant on-time control, it achieves an optimized efficiency and power factor over a large operation range.