This paper addresses the control problem of a three‐phase voltage source pulse width modulation rectifier in the presence of parametric uncertainties and external time‐varying disturbances. An adaptive controller is designed by combining a modified dynamic surface control method and a predictor‐based iterative neural network control algorithm. Especially, neural networks with iterative update laws based on prediction errors are employed to identify the lumped uncertainties. Besides, a finite‐time‐convergent differentiator, instead of a first‐order filter, is used to obtain the time derivative of the virtual control law. Using a Lyapunov–Krasovskii functional, it is proved that all signals in the closed‐loop system are ultimately uniformly bounded. Both simulation and experimental studies are provided to show the effectiveness of the proposed approach. © 2017 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.