A continuous fractional order sliding mode controller (CFOSMC) based on a developed output feedback feature selection neural network (OFFSNN) for an active power filter (APF) is studied in this paper to effectively compensate grid harmonic current and improve power quality. A fractional order sliding mode manifold is introduced firstly. Then a continuous fractional order sliding mode controller is adopted to resolve the shortcoming of chattering phenomenon in the conventional one by designing a continuous control law. Furthermore, considering the unknown part of APF system, a new neural structure called OFFSNN is established to estimate the unknown dynamic characteristic with high precision and low computational burden. Compared with general neural network, the proposed OFFSNN is adept at adjusting neural structure and parameters by selecting beneficial nodes as well as deleting useless ones. To demonstrate the effectiveness and superiority of the presented scheme, experiments in various cases on the APF platform are given.