In order to improve the dynamic response speed of the three-phase PWM rectifier when the load changes and reduce the AC current harmonics, an adaptive model predictive control strategy for the three-phase PWM rectifier is proposed. The control strategy consists of a nested DC side voltage controller and an AC side current controller. The DC side voltage controller estimates the change of the DC side load and adjusts the reference current of the AC side current controller in real time, so that the rectifier DC side voltage can make a fast dynamic response to the change of load and return to the set value. A multi-vector model predictive current controller was designed to reduce the harmonic spectrum dispersion of the AC side current caused by the switching frequency variation. Simulation experiments show that compared with the FCS-MPC strategy, the control strategy proposed in this paper can effectively shorten the startup process of the three-phase PWM rectifier, quickly respond to load changes, and improve the power quality on the AC side.