Liquid air energy storage (LAES) is a promising solution for overcoming the challenge of intermittency in renewable-based energy systems. Cold recovery is the most important part of the LAES and plays a vital role in the performance of the system. In this study, the LAES system which utilizes a packed bed thermal energy storage (PBTES) comprising three-layer phase change materials (PCM) is investigated from a thermodynamic and economic point of view. As a result of the transient nature of PBTES the dynamic modeling is applied to analyze the performance of the system. The designed LAES system with ideal condition consumes 4.42 MWh for compressing the air and generates 1.8 MWh of electricity during the peak time. The payback period of the system for the case study of San Fransico is 6.7 years with 0.66 M$ total profit. As a dynamic behavior of the system liquid yield, the mass flow rate of liquid air, the specific work of the compressors, and the cryo turbine vary during different cycles. After about 22 cycles system with a total efficiency of 42.5% reaches the equilibrium and the performance of the system decrease about 5.9% because of transient behavior in comparison with the ideal cycle