Nowadays, the selection of a suitable adaptive controller for a Distribution STATic COMpensator (DSTATCOM) is a tough job for the researchers due to the complexity of the power system. The performance of the DSTATCOM depends on the effectiveness of the control algorithm. This paper presents a Sparse Least Mean Square (SLMS) control algorithm for a three-phase DSTATCOM to mitigate the power quality problems. Specifically, the control algorithm is implemented to compensate current harmonics, reactive power and load unbalancing. The reference source currents are generated followed by extracting the weighted values of fundamental active and reactive power components of harmonic rich three-phase load current. The intention of the proposed control algorithm is to generate appropriate switching signals for the Voltage Source Converter (VSC) of the DSTATCOM in order to maintain its DC-link voltage constant. The simulation is performed in the MATLAB software.