This paper proposes an application of a least mean-square (LMS)-based neural network (NN) structure for the power quality improvement of a three-phase power distribution network under abnormal conditions. It uses a single-layer neuron structure for the control in a distribution static compensator (DSTATCOM) to attenuate the harmonics such as noise, bias, notches, dc offset, and distortion, injected in the grid current due to connection of several nonlinear loads. This admittance LMS-based NN structure has a simple architecture which reduces the computational complexity and burden which makes it easy to implement. A DSTATCOM is a custom power device which performs various functionalities such as harmonics attenuation, reactive power compensation, load balancing, zero voltage regulation, and power factor correction. Other main contribution of this paper involves operation of the system under abnormal conditions of distribution network which means noise and distortion in voltage and imbalance in three-phase voltages at the point of interconnection. For substantiating and demonstrating the performance of proposed control approach, simulations are carried on MATLAB/Simulink software and corresponding experimental tests are conducted on a developed prototype in the laboratory.