The transient behavior of DC-link voltage (DCV) significantly affects the low-voltage ride-through for phase-locked loop (PLL)-based grid-connected doubly-fed induction generator (DFIG) systems. This study investigates the DCV transient behavior of a PLL-based DFIG system under asymmetrical grid faults. First, by considering the coupling characteristics of positive and negative sequence (PNS) components, a nonlinear large-signal model of DCV is developed. Furthermore, the transient characteristics of DCV under varying parameters are analyzed using phase trajectory diagrams. In addition, the transient stability (TS) mechanism of DCV during asymmetrical faults is examined through an energy function approach. The analysis indicates that the transient instability of DCV is primarily associated with the control characteristics of PNS PLLs, while the TS level of DCV is mainly determined by the power coordination control between the rotor side converter and grid side converter. Moreover, a coordinated control strategy is proposed to enhance the TS of DCV under asymmetrical grid faults. Finally, both simulation and experimental results are presented to validate the theoretical analysis and the effectiveness of the proposed strategy.