The deadbeat predictive current control (DPCC) is weakened by the one-step control delay and model parameters mismatch issues in the permanent-magnet synchronous motors (PMSM) drive system. In order to acquire the high dynamic and static performance, this paper proposes a sliding-mode observer basing on adaptive super-twisting algorithm (ASTA-SMO) to improve DPCC method. First, the discrete-time model of PMSM considering the parameters mismatch is derived. Second, the conventional DPCC performance is analyzed when these two issues exist. Meanwhile, the second-order sliding-mode observer based on the super-twisting algorithm (STA-SMO) is constructed. Through the observer, the sampled current in DPCC is replaced by prediction currents to compensate one-step delay, and the estimated parameters disturbances compensate the voltage vector from DPCC. To further improve system dynamic performance and obtain stronger robustness, ASTA-SMO is proposed, which can vary the sliding-mode coefficients of STA-SMO online. Moreover, the switching function adopts hyperbolic tangent function to suppress the chattering. Finally, the proposed scheme is simulated, which is testified to have strong robustness and better current tracking performance with the load and motor parameters variations.