In this paper, a new structure for a multi-level switched-capacitor inverter with a combined phase shift switching method is proposed to reduce the number of components and voltage ripple and charging current of capacitors. The proposed structure combines a switching capacitor unit (SC) and a flying capacitor unit (FC). The advantages of the proposed structure include reducing number of devices, simplifying control, providing voltage boosting capability, and reducing voltage ripple and inrush current of capacitors with the proposed combined phase shift modulation. Applying the proposed modulation leads to the reduction of the maximum continuous discharge period. It reduces the voltage ripple and inrush current of the capacitors, which ultimately causes an effective reduction of the ripple and conductive losses. Ten switches, two diodes, and three capacitors are used to create 13 levels. The proposed structure, which has fewer devices than other 13-level inverters, does not require a capacitor with a high-rated voltage. The flying capacitor used in the proposed structure can naturally be balanced at half of the input DC voltage (0.5Vdc). Following the simple control of the voltage balance of the capacitors, this structure requires only five switching signals, which reduces the overall system cost. The circuit's performance, the proposed modulation scheme, the capacitors' automatic balancing, and their charging and discharging process have been investigated. Numerical comparison with recent 13-level inverters, shows the advantages of simple control, cost-effectiveness,, reduced voltage ripple and inrush current. Finally, simulation results are presented and analyzed to verify the validity of the proposed structure.