When a grid fault causes voltage sag, the rotor circuit of the doubly-fed induction generator (DFIG) may experience overcurrent, posing a threat to the safe operation of the converter. The research establishes a mathematical model of the DFIG under grid voltage sag conditions, analyzes the mechanism of rotor current overcurrent, and proposes a rotor overcurrent suppression strategy based on a vector proportional-integral (VPI) controller. The proposed strategy adds a control loop for the free component of rotor current to the conventional vector control framework. By designing a VPI controller specifically for the free component of the rotor current, it can quickly regulate this current component without the need for additional variable separation or reference value calculation, simplifying the design of control system. Simulation results demonstrate that the proposed control strategy effectively suppresses the rotor current overcurrent during grid voltage sag and enhances the low voltage ride-through capability of the DFIG.