A Finite Control Set Model Predictive Control (FCS-MPC) algorithm is proposed for an interleaved DC-DC boost converter as a current-mode controller to follow the inductor current reference without an additional modulation stage. It is able to ensure equal load distribution among the paralleled branches and overcome non-minimum phase behavior through transferring output voltage regulation into inductor current regulation. A Kalman observer is designed to obtain the load resistance variation and the integrated voltage error which is used to compensate the current reference calculation. The algorithm has been tested in simulation and the results show the proposed control strategy could achieve effective output voltage regulation with fast response and good robustness in the presence of load variations and input voltage disturbances.