With more and more distributed energy connected to the power system, the inverter needs to adopt a suitable control scheme to ensure the safety and stability of the system. Virtual synchronous generator (VSG) control algorithm can improve the stability of weak grid system to some extent by mimicking the dynamic characteristics of traditional rotary synchronous generator. However, when considering the frequency coupling effect, the impedance model of VSG needs to be established through complex matrix operation, which is inconvenient for system analysis and design, especially when the VSG system connects with asymmetric loads. In this paper, a recursive admittance matrix model for VSG system is proposed, which avoids complex matrix operations and convolution operations. At last, the accuracy of the recursive admittance matrix model and the correctness of the recursive modeling method are verified through Matlab/Simulink simulation.