Conventional primary control employs outer-loop droop and inner-loop cascaded linear control to realize local voltage regulation and power-sharing of an islanded ac microgrid. However, it has a complex structure, limited dynamic response, and a rapid rate of change of frequency when disturbances occur. This article resolves these issues by proposing a model predictive control-based virtual synchronous generator (VSG-MPC). An improved finite-set MPC is first proposed for the inner loop, achieving simplified control structure, faster dynamic response, enhanced bandwidth and stability, as well as improved current limitation. In the outer control loop, a simplified VSG without a phase-locked loop is employed to realize active power-sharing and inertia emulation. The merits above are verified by a description function of MPC and the frequency-domain response of the overall VSG. Simulation and experimental results verify the feasibility of the proposed method.