A distribution static compensator (DSTATCOM) is proposed in this study to improve the power quality, which includes the total harmonic distortion (THD) of the grid current and power factor (PF), of a mini grid with nonlinear and linear inductive loads. Moreover, the DC-link voltage regulation control of the DSTATCOM is essential especially under load variation conditions. Therefore, to improve the power quality and keep the DC-link voltage of the DSTATCOM constant under the variation of nonlinear and linear loads effectively, the traditional proportional-integral (PI) controller is substituted with a new online trained compensatory fuzzy neural network with an asymmetric membership function (CFNN-AMF) controller. In the proposed CFNN-AMF, the compensatory parameter to integrate pessimistic and optimistic operations of fuzzy systems is embedded in the CFNN. Furthermore, the dimensions of the Gaussian membership functions are directly extended to AMFs for the optimization of the fuzzy rules and the upgrade of learning ability of the networks. In addition, the network structure and online learning algorithm of the proposed CFNN-AMF are introduced in detail. Finally, the effectiveness and feasibility of the DSTATCOM using the proposed CFNN-AMF controller to improve the power quality and maintain the constant DC-link voltage under the change of nonlinear and linear inductive loads have been demonstrated by some experimental results.