Single-inductor multiple-output(SIMO) dc-dc converters have the advantages of less magnetic component count, small size and low cost. Under continuous conduction mode (CCM) for traditional SIMO converters, the control strategies are complex and high cost in order to solve the cross-regulation issue due to the inductor-sharing property. This paper adopts a current-source-mode(CSM) SIMO converter, which can guarantee good cross-regulation performance, without additional cost. The evolution and operation of this converter are discussed in detail. Further incorporating model predictive control(MPC) method, the steady-state and dynamic performance of the CSM SIMO converter are conducted in simulation. The comparison between MPC and traditional proportional-integral(PI) method is presented. Simulation results show that the MPC method can improve the dynamic performance as well as eliminate its cross-regulation issue. In addition, for the problem that the computational complexity of the CSM SIMO converter increases exponentially with the number of switches under MPC, this paper proposes a method of making tables offline and looking up tables online. By means of classification, the proposed method reduces the number of switching combinations to be traversed in each cycle, and simplifies the calculation process of the system. The calculation burden is reduced.