Deadbeat predictive current control for permanent magnet synchronous motors exhibits good dynamic and steady-state performance. However, it heavily depends on motor parameters, and if the motor parameters in the controller do not match the actual motor parameters, both its dynamic and steady-state performance will significantly deteriorate. To enhance the robustness of deadbeat predictive current control and eliminate the impact of parameter mismatches, a deadbeat predictive current control method based on an extended state observer with adaptive linear neurons is proposed. The linear extended state observer can accurately estimate slowly varying disturbances, but its disturbance observation speed is limited by the bandwidth of the observer, leading to significant steady-state estimation errors for harmonic disturbances. Adaptive linear neurons can adjust the filter coefficients through an adaptive algorithm, allowing the filter’s performance to adapt to changes in harmonics and noise. By combining these two approaches, it is possible to effectively estimate both slowly varying and harmonic disturbances in the system, thereby suppressing the impact of total disturbances on the system. The effectiveness of this method was validated through simulations by comparing it with traditional deadbeat predictive current control and deadbeat predictive current control based on an extended state observer.