When the load power of a microgrid fluctuates, the energy storage system can maintain the stability of the system voltage and frequency by controlling the inverter. Energy storage inverters commonly adopt a double closed-loop control strategy with PI algorithm, but due to the lag of PI control, the dynamic response speed of the system is slow. To address this issue, a finite control set-model predictive control (FCS-MPC) strategy considering Lyapunov stability constraints is proposed. Firstly, the main control objective which is the stable control of the capacitor voltage, is achieved through Lyapunov stability constraints, and weight coefficients are set based on the severity of the total harmonic distortion constraint term of the capacitor voltage. Then, collaborative control is achieved by minimizing the objective function, solving the problems of system instability caused by the coupling of traditional FCS-MPC objective functions and difficulty in tuning weight coefficients. The improved FCS-MPC scheme is combined with droop control to control the energy storage inverter. Finally, simulation verification is performed on the MATLAB and RT-LAB platforms. Simulation results show that compared with traditional control strategies, this approach can improve the dynamic response speed of the system, achieve multi-objective collaborative control, and exhibit good robustness to weight coefficients.