A robust wavelet neural network control (RWNNC) system is proposed to control the rotor position of an induction servo motor drive in this paper. In the proposed RWNNC system, a wavelet neural network controller is the main tracking controller that is used to mimic a computed torque control law, and a robust controller is designed to recover the residual approximation for ensuring the stable control performance. Moreover, to relax the requirement for a known bound on lumped uncertainty, which comprises a minimum approximation error, optimal network parameters and higher order terms in a Taylor series expansion of the wavelet functions, an RWNNC system with adaptive bound estimation was investigated for the control of an induction servo motor drive. In this control system, a simple adaptive algorithm was utilized to estimate the bound on lumped uncertainty. In addition, numerical simulation and experimental results due to periodic commands show that the dynamic behaviors of the proposed control systems are robust with regard to parameter variations and external load disturbance.