The integrated dc-link choke can replace the bulky transformer in current-source converter (CSC)-fed motor drive systems to bear the common-mode voltage (CMV). However, the common-mode (CM) resonance will be excited by the specific harmonics in the CMV, which causes excessive CM current in the loop. Moreover, due to the high-order filter, the $LC$ / $CL$ resonance is prone to be induced at the rectifier and inverter sides, respectively. In this article, the model predictive control (MPC) scheme is proposed to tackle the CM resonance and filter resonance simultaneously. In the low-speed region, besides restraining the peak-to-peak (PTP) magnitude of the CMV at the rectifier side, the third-order harmonic of the CMV generated by the inverter is extracted and then penalized in the cost function to further suppress the CM current. With the increase of the motor speed, the control objective of the inverter side controller switches to the PTP magnitude of CMV suppression because of the alleviation of the CM resonance. The capacitor voltage of both rectifier and inverter sides are regulated via the cost function as well, which can mitigate the current harmonic distortion and improve system stability. The simulation with 1MVA rated power and the scaled-down experiment shows that the proposed scheme can suppress both the CM resonance and the $LC$ / $CL$ resonance effectively with a low switching frequency.