In order to ensure the effect of finite control set model predictive control (FCS-MPC) on power converter operation, the sampling frequency is generally set to 10~50kHz. However, the actual switching frequency is only 10-20% of the sampling frequency due to the phenomenon that the same switching state will be output for multiple consecutive sampling cycles, which affects the control accuracy. In the application scenarios of SiC, GaN and other high-speed devices, blindly increasing the sampling frequency to achieve high switching frequency output will cause great computing burden on the digital processor. To solve these problems, a multi-rate model predictive control(MR-MPC) method is proposed in this paper. A dual-rate MR-MPC discrete predictive model with low sampling input and high control output is constructed, and multi-level recursive optimization technology is introduced. Achieve a balance between computing burden and control performance. Finally, a 5kW motor test platform is built for experimental verification and analysis. MR-MPC inherits the ability of traditional FCS-MPC to deal with complex control targets, and can realize multi-rate frequency doubling of output switching frequency under the condition of low computation burden. The higher the frequency doubling ratio, the better the dynamic and steady state performance of the system. It can be regarded as one of the general design methods of high switching frequency power converter.