Grid faults are found to be one of the major issues in renewable energy systems, particularly in wind energy conversion systems (WECS) connected to the grid via back-to-back (BTB) converters. Under such faulty grid conditions, the system requires an effective regulation of the active (P) and reactive (Q) power to accomplish low voltage ride through (LVRT) operation in accordance with the grid codes. In this paper, an improved finite-control-set model predictive control (FCS-MPC) scheme is proposed for a PMSG based WECS to achieve LVRT ability under symmetrical and asymmetrical grid faults, including mitigation of DC-link voltage fluctuation. With proposed predictive control, optimized switching states for cost function minimization with weighing factor (WF) selection guidelines are established for robust BTB converter control and reduced cross-coupling amid P and Q during transient conditions. Besides, grid voltage support is provided by grid side inverter control to inject reactive power during voltage dips. The effectiveness of the FCS-MPC method is compared with the conventional proportional-integral (PI) controller in case of symmetrical and asymmetrical grid faults. The simulation and experimental results endorse the superiority of the developed FCS-MPC scheme to diminish the fault effect quickly with lower overshoot and better damping performance than the traditional controller.