Abstract: With the development of new power systems, grid-connected converters have become key pieces of equipment for energy transmission. The virtual synchronous machine parameters of model predictive control have low robustness,and when the parameters are mismatched, the output current ripple increases, and the synchronous machine power support decreases. To address this issue, an improved virtual synchronous model-free parameter robust predictive control method is proposed. This method first uses a fourth-order Runge-Kutta optimization super-local model-free method to obtain a robust model that enhances the virtual synchronous machine parameters. Then, the Lagrange interpolation method is used to solve the K parameter in the model, and the output for the next moment is predicted using the sampling values from the previous four moments. Also, a virtual inertia model-free adaptive prediction algorithm is designed to achieve dynamic response to inertia dynamic demand. Finally, the optimal voltage vector for virtual synchronous machines is obtained by optimizing the value function, achieving robust parameter-enhanced control. Experimental results show that the proposed control strategy has stable power support capability under parameter mismatch, and the virtual inertia can dynamically respond to frequency fluctuations, with good steady-state and dynamic response performance.