The single-phase split-source inverter （SSI） is a new and highly compact boost inverter with a topology consisting of a DC-link capacitor, a boost inductor, two diodes, and a conventional voltage-source inverter （VSI）. However, the conventional space vector pulse-width modulation （SVPWM） strategy leads to a large ripple in the passive element. In addition, the ripple of the passive element under the conventional sliding mode control （SMC） strategy has large jitter and the output voltage quality of the SSI system is low. In this paper, a finite control set⁃sliding mode control （FCS-SMC） strategy based on multi-objective cost function （MOCF） is proposed to address the problems of complex modulation, large jitter of sliding mode control and low quality of output voltage in SSI. The control of inductor current and capacitor voltage in the DC side, as well as the control of inductor voltage and capacitor current in the AC side of the SSI is essential, and the proposed control strategy based on MOCF FCS-SMC control method can accomplish the control of both DC-side and AC-side variables due to the use of MOCF functions. In addition, the use of finite control set eliminates the requirement of modulation scheme and the use of multi-objective cost function with FCS simplifies the design of the controller. The robustness of the proposed control strategy to parameter variations is investigated and compared with the conventional SMC based approach. Simulation and experimental results show that the proposed FCS-SMC strategy can effectively suppress ripple and reduce jitter to improve the output power quality of SSI.