For high-power or high-speed motor drives, the low switching frequency to fundamental frequency ratio leads to poor bandwidth or even instability of the current control loop if the controller is not properly designed. In this paper, a digital predictive current controller is constructed based on an exactly discretized model to overcome this issue. Then, a method of online disturbance adaptation is proposed to compensate for the side impact of motor parameter mismatches on the tracking performance. Additionally, online inductance adaptation is further incorporated to improve transient performance. Compared with the prior complex-vector proportional-integral controller, the proposed current controller presents faster dynamic responses and better parameter robustness. Simulation and experimental tests on a permanent magnet synchronous motor drive confirm the effectiveness of the proposed control schemes.