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This study presents a model predictive control (MPC) with active damping function for current-source rectifiers (CSRs). Since optimal modulating vector selection process of MPC leads to spread harmonic distribution in pulse-widthmodulated (PWM) waveform, inductor-capacitor (LC) resonance can be easily excited. Conventional MPC was designed without the consideration of active damping, since it is for low-power CSRs with large line resistors physically connected inside the circuit, whereas the proposed scheme achieves active damping function through a specially developed cost function, which realizes active damping function even for high-power CSRs with lightly damped LC circuit. In comparison with conventional MPC, the advantages of the proposed scheme are threefold: first, the proposed scheme is totally based on MPC concept, without conventional linear controller used. Second, with the active damping term added in the developed cost function, active damping effect can be involved into MPC, which extends MPC to high-power CSRs with lightly damped LC circuit. Last but not least, the proposed scheme is realized in the dq-axis synchronous frame, which allows the use of simple low-pass filters instead of complex band-stop filters to obtain the damping current.