An intelligent integral backstepping sliding-mode control (IIBSMC) system using a recurrent neural network (RNN) is proposed for the three-dimension motion control of a piezo-flexural nanopositioning stage (PFNS) in this study. Moreover, the RNN estimator is proposed to estimate the lumped uncertainty including the system parameters and external disturbance online. Furthermore, the online tuning law for the training of the parameters of the RNN is derived using the Lyapunov stability theorem. In addition, a robust compensator is proposed to confront the minimum reconstructed error occurred in the IIBSMC system. Finally, some experimental results are given to demonstrate the validity of the proposed IIBSMC system. From the performance measurings of the proportional-integral (PI) control, sliding mode control (SMC), integral backstepping sliding-mode control (IBSMC) and IIBSMC systems, the proposed IIBSMC system has the lowest maximum, average and standard deviation of the position tracking errors for the three-dimension motion control of the PFNS.