In this paper, a novel optimal adaptive-gains super-twisting sliding-mode control (OAGSTSMC) using actor-critic approach is proposed for a high-speed permanent-magnet synchronous motor (PMSM) drive system. First, the super-twisting sliding-mode controller (STSMC) is adopted for reducing the chattering phenomenon and stabilizing the PMSM drive system. However, the control performance may be destroyed due external disturbances and parameter variations of the drive system. In addition, the conservative selection of the STSMC gains may affect the control performance. Therefore, for enhancing the standard super-twisting approach performance via avoiding the constraints on knowing the disturbances as well as uncertainties upper bounds, and to achieve the drive system robustness, the direct heuristic dynamic programming (HDP) is utilized for optimal tuning of STSMC gains. Consequently, an online actor-critic algorithm with HDP is designed for facilitating the online solution of the Hamilton-Jacobi-Bellman (HJB) equation via a critic neural network while pursuing an optimal control via an actor neural network at the same time. Furthermore, based on Lyapunov approach, the stability of the closed-loop control system is assured. A real-time implementation is performed for verifying the proposed OAGSTSMC efficacy. The experimental results endorse that the proposed OAGSTSMC control approach achieves the PMSM superior dynamic performance regardless of unknown uncertainties as well as exterior disturbances.