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The typical finite-set model predictive control (FS-MPC) scheme for LC-filtered voltage source inverters (VSIs) lack inertia and damping, and the output current is easy to exceed the limit under the load-step change. Meanwhile, since the current sensor is needed to measure current information, the hardware cost is increased. To resolve these problems, an improved model predictive control combined with a virtual synchronous generator (MPC-VSG) is proposed in the paper. Above all, an MPC with a multi-objective cost function (CF) is used to minimize the tracking voltage error while providing overcurrent protection. Then, to provide the inertia and damping needed by the system, a VSG scheme is employed to generate voltage reference. Besides, a Luenberger observer is utilized to observe the inductor current. In this way, the number of current sensors is reduced to save the hardware cost. Finally, some comparative simulation experiments in Simulink verify the effectiveness of the improved MPC-VSG.