The electricity grid with high-penetration renewable energy sources has urged us to seek means to solve the mismatching between electricity supply and demand. Energy storage technology could accomplish the energy conversion process between different periods to achieve the efficient and stable utilization of renewable energy sources. In this paper, a hybrid energy storage system based on compressed air energy storage and reversible solid oxidation fuel cell (rSOC) is proposed. During the charging process, the rSOC operates in electrolysis cell (EC) mode to achieve the energy storage by converting the compression heat to chemical fuels. During the discharging process, the cell operates in fuel cell mode for electricity production and the gas turbine is conducted to recover the waste heat from cell. To evaluate the comprehensive performance of the proposed system, the energy, exergy, and exergoeconomic studies are conducted in this paper. Under the design condition, the results indicated that the proposed system is capable of generating 300.36 kW of electricity and 106.28 kW of heating; in the meantime, the energy efficiency, exergy efficiency, and total cost per unit exergy of product are 73.80%, 55.70%, and 216.78 $/MWh, respectively. The parametric analysis indicates that the increase in pressure ratio of air compressor, steam utilization factor of rSOC stack under EC mode and current density of the rSOC stack under EC mode reduce exergy efficiency and total cost per unit exergy of product simultaneously, while the increment of operating pressure of rSOC stack under FC mode enhances the exergy efficiency and decreases total cost per unit exergy of product. The multi-objective optimization is carried out to improve the comprehensive performance of the proposed system, and the results expressed that the best optimal solution has the exergy efficiency and total cost per unit exergy of product of 65.85% and 187.05 $/MWh, respectively. Compared to the basic operating condition, the improvement of the proposed system has led to the maximum enhancement of 20.32% in exergy efficiency and 18.60% in total cost per unit exergy of product.