Virtual synchronous generator (VSG) is a grid-friendly converter that can effectively support the grid and operate stably in a weak grid. However, VSGs are susceptible to grid voltage sags, which may induce overcurrent and transient instability due to their synchronous generator-like properties. In particular, as grid strength decreases, the output capacity of the VSG is reduced, making transient instability a more severe issue than overcurrent when a voltage sag occurs. Transient instability poses a threat to power system security and stability. To address these issues, a mechanism analysis and an advanced control strategy are proposed for VSGs operating under weak grid conditions during low-voltage ride-through (LVRT). First, the factors influencing transient stability are analyzed. Second, the characteristics of LVRT-related issues in weak grid conditions are examined. Finally, an advanced LVRT control strategy and a novel virtual impedance (Ⅵ) structure are proposed to maintain transient stability and suppress overcurrent. Benefiting from this strategy, transient stability is improved, and the post-fault period is expected to be short and smooth. Simulations and experiments are conducted to verify the effectiveness of the proposed approach.