Liquid storage tank is widely used in the petrochemical industry, earthquake will lead to structural damage and secondary disasters, and damping control opens up a new way for seismic design of liquid storage tank. Considering soil-structure-fluid interaction, liquid sloshing dynamic behavior and material nonlinearity, a three-dimensional calculation model of shock absorption liquid storage tank is established by combining sliding isolation and displacement-limiting devices. The dynamic responses of the liquid storage tanks under the action of Kobe and El-Centro waves are investigated, and the influence of soil-structure interaction (SSI) on the dynamic response is discussed. The results show that the damping ratio is basically between 30% and 90%. After the SSI is considered, the damping ratio of liquid sloshing wave height is increased, while the damping ratio of the dynamic response of the liquid storage tank is decreased, and the change of elastic modulus has little effect on the damping effect. The sliding isolation with displacement-limiting devices has significant damping control effects on the liquid sloshing wave height and the dynamic responses of the liquid storage tank.