An intelligent second-order sliding-mode control (I2OSMC) using a wavelet fuzzy neural network with an asymmetric membership function (WFNN-AMF) estimator is proposed in this study to control a six-phase permanent magnet synchronous motor (PMSM) for an electric power steering (EPS) system. First, the dynamics of the steer-by-wire (SBW) EPS system and six-phase PMSM drive system with a lumped uncertainty are described in detail. Then, to alleviate the chattering phenomena in a traditional sliding-mode control (SMC), a second-order sliding-mode control (2OSMC) is designed. Moreover, the I2OSMC is developed to improve the required control performance of the EPS system. In the I2OSMC, the WFNN-AMF estimator with accurate approximation capability is employed to estimate the lumped uncertainty. Furthermore, the adaptive learning algorithms for the online training of the WFNN-AMF are derived using the Lyapunov theorem to guarantee the asymptotical stability of the closed-loop system. In addition, a 32-bit floating-point digital signal processor (DSP), i.e., TMS320F28335, is adopted for the implementation of the proposed control approach. Finally, some experimental results are illustrated to demonstrate the validity of the proposed I2OSMC using the WFNN-AMF estimator for the EPS system.