Doubly Fed Induction Generator (DFIG)-based wind turbine as a nonlinear, compound and multivariable time-varying system encompasses several uncertainties especially unfamiliar disturbances and unmodelled dynamics. Design of a high performance and reliable controller for this system is regarded as a complex task. In this paper, an effective and roust Fractional Order Sliding Mode Controller (FOSMC) has been designed to accurately regulate the active and reactive power of DFIG. FOSMC has overcome the system uncertainties and abated the chattering amplitude. Since tuning the FOSMC is a challenging assignment, application of a multi-objective optimization algorithm can efficiently and precisely solve the design problem. In this regard, non-dominated sorting Multi-Objective Grey Wolf Optimizer (MOGWO) is taken into account to optimally adjust the FOSMC. In a word, the simulation results have definitively validated the robustness of MOGWO-based FOSMC in order to accurate tracking of DFIG's active and reactive power.