The installment of LC filter between the voltage source inverter 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. Conventional active damping (AD) scheme mainly introduce the multiloop feedback based on the analysis in s-domain or z-domain, which is realized with limited bandwidth and high tuning complexity. 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 a simplified form that suits the implementation of the digital platform, and the lower computational burden is obtained. The experimental results prove that the proposed FCS-MPC scheme can ensure the motor-friendly waveform and overcome the resonance problem effectively. The robustness of the controller to parameter variations of the filter is also verified.