Low-voltage ride-through (LVRT) capability of the doubly fed induction generator (DFIG) is seen as insufficient under severe grid faults due to it being prone to suffering from overcurrent. Especially in the asymmetrical grid faults, large oscillations of electromagnetic torque and output power of DFIG will also be caused. To suppress electromagnetic torque oscillation and improve DFIG system LVRT capability, the rotor current reference value should be set to follow the stator flux under severe asymmetrical grid faults. However, the stator flux contains AC components in the synchronous reference frame under asymmetrical grid faults. The classical proportional-integral controller cannot accurately track AC references. To solve this problem, a model predictive control (MPC) method for the DFIG rotor-side converter in the stationary reference frame was proposed in this paper. With this proposal, the tracking accuracy of the rotor current reference value has been considerably improved under asymmetrical grid faults. Thus, the electronic torque oscillation has been reduced to a large extent, and the DFIG system LVRT capability was improved. Finally, simulations verified the effectiveness of the proposed method.