The installment of LC filter between the voltage source inverter (VSI) and motor terminal can reduce the value of dv/dt considerably, and further mitigate the surge voltage stress on the motor windings during the long-distance transmission. However, the sophisticated controller needs to be designed to solve the additional resonance problems caused by the filter. In this article, the finite-control-set model predictive control (FCS-MPC) is adopted to realize the q-axis current reference tracking for motor and suppress the filter resonance simultaneously. Different from the transfer-function-based AD scheme, the mechanism of resonance generation is revealed in the time-domain, where the cost function of FCS-MPC is designed to directly regulate the multivariable trajectory of the system. Therefore, the proposed FCS-MPC controller expresses the intuitive design principle, a simple structure, and fewer tuning parameters, which could be an alternative to the existing AD scheme. To reduce the number of sensors, the Kalman-filter based state estimation is used by considering the one-step delay of the control input. The cost function is further optimized to obtain a lower computational burden. The experimental results prove that the proposed FCS-MPC scheme can ensure the motor-friendly waveform and overcome the resonance problem effectively.