In power conversion applications grid synchronization systems should face very different network operating conditions such as: generic grid connection, faulty or distorted scenarios or islanded conditions among others. However, all the existing synchronization systems have issues operating in all these scenarios if the control tuning parameters cannot be adapted to the grid conditions. This paper proposes a Fuzzy Gain Scheduling PLL (FGS-PLL) to be used for grid synchronization, which has a robust performance in case of severe voltage sag, where there is even a null value of voltage, and phase jump conditions. Moreover, the proposed method employs a fuzzy gain scheduling technique to adjust the proportional and integral gains of the proposed PLL during amplitude, phase and frequency variations in the grid voltage waveform to build a flexible PLL in case of severe grid conditions. This PLL structure permits to adjust the performance in different conditions as well as to provide a voltage reference, even in case of 100% voltage sag.