This paper deals with a control design based on amplitude adaptive notch filter (AANF) for a four-leg distributed static compensator (DSTATCOM) in a three-phase four-wire distribution grid to overcome current-related problems of power quality. Extractedreference currents ofDSTATCOM are obtained usingAANF because of its simple structure, exactmeasuring of frequency and amplitude, suitable estimation of the desired signal, and capability of tracking the changes of the input signal amplitude. To improve the dynamic performance of DSTATCOM, two fuzzy logic controllers are utilized to regulate DC link voltage and the voltage of point of common coupling (PCC). Furthermore, an adaptive hysteresis band current controller is applied for generating the gate pulses of IGBT switches. The proposed control scheme is robust to power system oscillations, especially when the main voltage suffers from disturbances and unbalancing. Different surveys are performed to study the efficacy of the proposed method, and results are verified through the simulation results in MATLAB/Simulink environment.