As permanent magnet synchronous generator (PMSG) based wind farm is connected to the weak receiving-end AC grid, the dynamic instability arising from the complicated interaction between the receiving-end AC grid and the wind farm has been a concerned issue in the PMSG-based Grid-connected wind energy conversion system (PMSG-WECS). To assess the dynamic stability accurately, an improved dynamic short circuit ratio (IDSCR) is proposed. Firstly, to consider the impact of the time delay, an equivalent discrete time-varying state space model of PMSG-WECS is built based on exact discretization method and linear fitting. By decomposing it into several subsystems, a generalized gain matrix constructed with the gain coefficients of the finite-step inequalities is proposed to quantify the effects of the interactions between diverse subsystems. Based on the generalized gain matrix, the IDSCR, whose critical value is a constant value, is defined to analyze the dynamic stability of the PMSG-WECS. The mathematical relation between the dynamic stability and proposed IDSCR is established from the perspective of the input-state stability (ISS). Finally, the IDSCR is verified by implementing the time-domain simulation and multiple comparative researches.