The next generation of power system is expected to be more complex and sensitive. Therefore, controllers implemented for a custom power device must be efficient and adaptive. In order to mitigate the power quality problems, a Modified Leaky Least Mean Square (MLLMS) control algorithm for a three-phase Supercapacitor based Shunt Active Power Filter (SSAPF) is proposed in this paper. Especially, the efficient control algorithm meant for power quality improvement by compensating source current harmonics, load unbalancing and reactive power flow in the system. Suitable switching pulses required for Voltage Source Converter (VSC) of the SSAPF are generated followed by the reference current generation and extraction of fundamental active and reactive power components from harmonic rich three-phase load currents. The supercapacitor is coupled with the VSC to make the DC-link voltage constant and ripple free during faults in the system. The performance of the SSAPF using a MLLMS control algorithm is conducted in the MATLAB software.