This paper introduces a novel Model Predictive Control (MPC)-based strategy to enhance Low-Voltage Ride-Through (LVRT) capability for wind turbines equipped with Doubly Fed Induction Generators (DFIGs). According to modern grid codes, grid-connected wind turbines must remain operational during voltage dips and support the grid by injecting both active and reactive power. However, voltage dips pose significant challenges for (DFIG)-based wind turbines because voltage dips can induce significant large inrush current in the rotor, potentially damaging the rotor converter. Conventional control methods employ proportional-integral (PI) controllers for rotor current regulation and crowbar circuits to protect the converter by diverting high rotor currents away from the converter when they exceed their safe limit. While effective in protecting the hardware, crowbar activation temporarily disconnects the rotor from control, leading to a loss of power injection capabilities and noncompliance with grid codes. To overcome these limitations, this paper proposes an MPC-based rotor current controller formulated as a Quadratically-Constrained Quadratic Programming (QCQP) optimization problem. This controller explicitly incorporates rotor current and voltage constraints while optimizing control performance during grid faults. MATLAB-based simulations for both low- and medium-voltage dips demonstrate the superiority of the proposed approach over conventional PI controllers. The results confirm that the MPC strategy ensures LVRT compliance without the need for a crowbar circuit, maintaining stability and improving performance during a wide-range of fault conditions.