As a core propulsion device for spacecraft, the liquid rocket engine relies heavily on its electro-mechanical actuation system (EMAS) for precise thrust regulation and control. Permanent magnet synchronous motors (PMSM) are widely applied in EMAS. However, traditional proportional-integral (PI) current control exhibits inherent limitations when confronted with variations in motor electrical parameters. Accordingly, research on model predictive control (MPC) for PMSM is conducted in this paper.The mathematical models of PMSM in different coordinate systems are established, and predictive speed and current control strategies are designed based on the fundamental principles of MPC, including the corresponding prediction models and cost functions. A simulation model is built on the MATLAB/Simulink platform to compare the performance of MPC with field-oriented control (FOC). Simulation results show that compared with FOC, MPC reduces the steady-state error by approximately 99%, eliminates overshoot, and shortens the response time by about 80% in position step response. It delivers superior dynamic tracking capability under swept-frequency input and cuts the speed fluctuation amplitude by around 80% under variable load conditions. Experimental verification is carried out on a motor back-to-back test platform. The test results prove that MPC achieves smoother response and smaller oscillation when the input signal changes, and possesses stronger adaptability to large load disturbances. Applied to PMSM control in the EMAS of liquid rocket engines, MPC delivers better control performance, effectively improves the overall control effect of the EMAS, and provides an optimized solution for relevant engineering applications.