For phase-shifted full-bridge converters used in on-board power systems of electric vehicles operating under a wide input voltage range, conventional control strategies suffer from poor dynamic performance and large overshoot. To address these issues, an improved control strategy that combines model predictive control with load current feedforward compensation is proposed. Firstly, the operational principles of the transformer lagging(Tr-lag) zero voltage switching(ZVS) phase shifted full bridge converter and the mechanism of duty cycle loss are analyzed. On this basis, a mathematical model is established to decouple the control variable from the duty-cycle loss, from which the steady-state operating model of the converter is derived. Secondly, to address the degradation in converter model accuracy and system dynamic performance caused by duty cycle loss, an enhanced mathematical model for model prediction control is derived and applied to the current inner loop. Meanwhile, a duty-cycle compensation mechanism is introduced, which effectively improves the accuracy of the converter model and the dynamic performance of the system. Furthermore, by establishing a system load estimation model and incorporating load current feedforward compensation into the voltage outer loop, the excessive output voltage overshoot caused by sudden load changes is effectively suppressed. Finally, comparative experiments are conducted to evaluate the proposed control strategy against both traditional dual-loop control and sliding mode control strategies Experimental results demonstrate that, when the proposed control strategy is applied to a Tr-lag ZVS phase-shifted full-bridge converter, both output voltage overshoot and undershoot during load transients are suppressed to within 10% of the reference voltage across the entire wide input voltage range of 300~800 V, with recovery times limited to within 5 ms. These results indicate that the proposed control strategy effectively enhances the converter′s adaptability to different battery voltage levels in electric vehicles, thereby validating its feasibility and superiority and providing innovative theoretical insights and practical engineering references for on-board power supply systems.