In response to the high cost and large size issues associated with traditional back-to-back three-level inverters, this paper proposes a novel dual-port three-level inverter(DP-TLI) that simplifies the system structure through the utilization of switch multiplexing. Based on the proposed inverter topology, a time-sharing coordination finite control set model predictive control(TSC-FCS-MPC) strategy is developed. The strategy, grounded in the concept of time-sharing control, incorporates a coordinated approach within a two-cycle control loop. During the first cycle, the primary control objective is to optimize the output current of the upper port, with the selection of the optimal vector centered around this goal. Subsequently, the lower port's output is coordinated through control, leveraging the unique aspects of switch multiplexing and the redundancy in switch states inherent in the proposed topology. In the second cycle, the emphasis is reversed, with the optimization of the lower port's output current taking precedence, while the upper port is subjected to coordinated control. The implementation of this method significantly enhances the quality of the output current and the overall efficiency of the system. The viability and effectiveness of both the proposed topology and the control strategy are confirmed through simulation and experimental results.