To address the problem of insufficient system inertia and improve the power quality of grid-connected inverters, and to enhance the stability of the power system, a method to control a virtual synchronous generator (VSG) output voltage based on model predictive control (MPC) is proposed. Parameters of the inductors, capacitors and other components of the VSG can vary as the temperature and current changes. Consequently the VSG output voltage and power control accuracy using the conventional MPC method may be reduced. In this paper, to improve the parameter robustness of the MPC method, a new weighted predictive capacitor voltage control method is proposed. Through detailed theoretical analysis, the principle of the proposed method to reduce the influence of parameter errors on voltage tracking accuracy is analyzed. Finally, the effectiveness and feasibility of the proposed method are verified by experimental tests using the Typhoon control hardware-in-the-loop experimental platform.