This paper presents a Modified Leaky Least Mean Square (MLLMS) control algorithm for a three-phase Supercapacitor based Shunt Active Power Filter (SSAPF) to mitigate the power quality problems in the grid. Specially, alleviation of Source current harmonics, reactive power, and load unbalancing in the system are realised by the efficient control algorithm. The tuned weighted values of fundamental active and reactive power components of harmonic rich three-phase load current are extractedin order to generate reference source currents. After that, the switching signals for the Voltage Source Converter (VSC) of the SSAPF are generated to maintain its DC-link voltage constant. Also, the Supercapacitor is coupled with the VSC maintain constant DC-link voltage and eliminates the ripple during faults in the system. The performance of the SSAPF using MLLMS control algorithm is carried out using MATLAB/Simulink software.