Compressed air energy storage (CAES) technology is one of the important technologies to address the instability of renewable energy sources. To further make full use of the system heat of compression and reduce the problem of energy grade dissipation inside the accumulator, this paper proposes a novel CAES system coupled with a graded phase change thermal energy storage unit (SP-TES) and near isothermal compression of a liquid piston. A combination of adiabatic compression and near-isothermal compression is used to reduce the generation of compression heat, while the graded storage of compression heat through SP-TES reduces the reduction of energy grade. The design of the proposed SP-TES is carried out through the binary eutectic theory, and a one-dimensional transient entransy dissipation model, a thermodynamic model and an economic model are developed to analyze the 4E performance (energy, exergy, entransy, and exergoeconomic) of the proposed SP-TES. Further, the effect patterns of key node parameters on the proposed system are investigated by developing system related models and the system is optimized with multiple objectives from the point of view of economic and thermodynamic performances. The results show that the 4E performance of SP-TES is in between that of high and low temperature single-stage accumulators, and that SP-TES combines the advantages of higher economic performance of single-stage low-temperature accumulators and higher thermal performance of single-stage high-temperature accumulators. The SP-TES with a temperature range of 350 K-451 K is gradually stabilized with the number of charging and discharging, and the efficiency of the system in the stabilization stage is 73.24 %. The SP-TES with a temperature range of 407 K-440 K has the best economic performance with exergoeconomic parameter of 360.05 kJ/USD. The thermal storage performance and power output of the SP-TES decreases with the increase in the number of stages. The multi-objective optimization results show that the new CAES system efficiency is 63.03 % and the design is optimal when the unit energy cost is 0.2217 $/kWh.