In permanent-magnet synchronous machine (PMSM) applications, traditional deadbeat predictive current control (DPCC) utilizes the PMSM model to evaluate the expected voltage vector and applies it to the inverter through space vector pulse width modulation (SVPWM). Once the expected voltage vector is inaccurate, the torque ripple and speed fluctuation are amplified. There are two main factors that cause the inaccurate voltage vector, namely model parameter mismatch, and current measurement error. To enhance the robustness of DPCC, first, this paper proposes an accurate PMSM voltage model with nonperiodic and periodic disturbance models. Second, this paper proposes a novel current and disturbance observer (NCDO) which is able to predict future stator currents and disturbances caused by model parameter mismatch and current measurement error simultaneously. Finally, the scheme of the proposed DPCC with NCDO is presented to enhance the robustness. This paper presents a comparative study of two types of algorithms, namely traditional DPCC and the proposed DPCC with NCDO. The theoretical verification, simulation results, and experimental results are demonstrated to verify the effectiveness of the proposed DPCC with NCDO.