A low root mean square (RMS) current flowing through the intermediate DC-link capacitor is always desired in the back-to-back (BTB) voltage source converters (VSCs)-fed motor drive, such that the designed capacitor lifespan can be extended or a lower DC-link size could be the alternative with improved power density. The conventional modulator-based control involves the inherent carrier-based switching operation, and hence the dominant harmonics at carrier frequency multiplier and carrier sideband are introduced into the capacitor current. Therefore, the finite-control-set model predictive control (FCS-MPC) is proposed to optimize the capacitor RMS current. The direct switching pulse generation without using the carrier can give a distinctive capacitor current spectrum and more possible current pulse cancellation between the BTB VSCs can be conveniently achieved through the cost function. Besides, the acceptable grid-current quality and the motor performance are maintained by using a tunable weighting factor. The simulated and experimental results highlight the effectiveness and benefits of the proposed method in terms of 20%-35% capacitor RMS current reduction compared to the synchronous carrier-based space vector pulse-width modulation (SVPWM) scheme and also significant improvements over the distributed predictive manner.