In addressing the transient synchronization issue of grid-connected virtual synchronous generator considering current limiting strategies, traditional methods often rely on algebraic variable switching rules based on current amplitude. These methods make it difficult to analytically analyze the instability mechanisms, and the proposed criteria are also quite conservative. To tackle these issues, this paper introduces a switching model based on state variables using current limiting inequalities as a starting point. A transient stability criterion based on the multiple Lyapunov method is then proposed. This states that the system can remain stable if the Lyapunov functions of each subsystem exhibit a decreasing trend over two consecutive switching intervals. Finally, a method for setting the current limiting parameters is presented to maximize the system’s stability boundary. Simulation results demonstrate that the proposed criteria are less conservative than the equal-area method, and the effectiveness of the conclusions drawn in this paper is verified.