In the case of a high penetration rate of wind energy conversion systems, the conventional virtual inertia control of permanent magnet synchronous generators (PMSG) has an insufficient support capability for system frequency, leading to an unstable system frequency and a slower response. Considering the finite control set model predictive control has multi-objective regulation capabilities and efficient tracking capabilities, and an improved multi-objective model-predictive control is proposed in this paper for PMSG-based wind turbines with virtual inertia based on its mathematical model. With the prediction model, the optimal control of the current and the frequency of the PMSG-based wind turbines can be obtained. Since the shaft torque changes rapidly under high virtual inertia, shaft oscillation may occur under this scenario. To address this problem, the electromagnetic torque is set as an additional optimization objective, which effectively suppresses the oscillation. Furthermore, based on accurate short-term wind speed forecasting, a dynamic weight coefficient strategy is proposed, which can reasonably distribute the weight coefficients according to the working conditions. Finally, simulations are carried out on a 2 MW PMSG-based wind turbine platform, and the effectiveness of the proposed control strategies is verified.