The transient synchronization characteristics and instability mechanism of the permanent magnet synchronous generator (PMSG)-based grid-forming wind energy conversion system (GFM-WECS) under symmetrical grid fault have received little attention to date. In this paper, considering the dynamics of DC-link voltage, the transient stability and an improved control strategy of PMSG-based GFM-WECS are studied in detail. Firstly, considering the dynamic interactions between the machine-side converter and the grid-side converter, the large-signal equivalent model of GFM-WECS is established. Furthermore, a novel Lyapunov function is derived to evaluate the transient stability margin and instability boundary of GFM-WECS during grid voltage sag. Additionally, the impacts of current-limitation control on the transient stability of GFM-WECS are revealed. Then, a stability evaluation index is proposed to evaluate the transient stability margin of GFM-WECS. Moreover, an improved control strategy is proposed to enhance the transient response characteristics and low voltage ride-through (LVRT) capability of GFM-WECS under symmetrical grid fault. Finally, simulations and experimental results are conducted to verify the effectiveness of the proposed control strategy.