Due to the instantaneous power following into or out of the DC-link capacitor in a three-phase shunt active power filter (APF), the DC-link voltage regulation control plays an important role in the shunt APF especially under nonlinear load change. In this paper, for the purpose of improving the DC-link voltage regulation control in the shunt APF under nonlinear load variation and reducing the total harmonic distortion of the current effectively, a novel recurrent probabilistic fuzzy neural network with an asymmetric membership function (RPFNN-AMF) controller is developed to substitute for the conventional proportional-integral controller. Moreover, the network structure, the online learning algorithm, and the convergence analysis of the proposed RPFNN-AMF are detailedly introduced. Finally, the effectiveness and feasibility of the shunt APF using the proposed RPFNN-AMF controller for the DC-link voltage regulation control and the compensation of harmonic current are verified by some experimental results.