It is necessary to ensure the safety of liquid storage tanks under earthquakes, but the damage probability of the non-damping liquid storage tanks is higher under earthquakes. Based on the damping principle of tuned mass damper (TMD) and the characteristics of the liquid storage tank, a new pendulum TMD (PTMD) system is proposed. Considering the material nonlinearity, the fluid–structure interaction and liquid sloshing characteristics, the three-dimensional numerical calculation models of the non-damping, PTMD, base-isolation (BI) and BI-PTMD liquid storage tanks are established, respectively. The seismic responses of different types of liquid storage tanks under the action of near-field pulse-like earthquakes are investigated, the damping performance of the hybrid control system with the isolation and the PTMD is analyzed, and the influence laws of the mass ratio of PTMD-structure and base-isolation period on the dynamic responses of the liquid storage tanks are discussed. The results show that the BI-PTMD hybrid control system has a significant damping effect on the seismic responses of the liquid storage tank. The damping rate of the base shear is the largest, reaching 86.0%, and the control rate of the PTMD on the displacement of the isolation layer is about 20.0%. The hoop stress, effective stress, liquid pressure and displacement of isolation layer decrease with the increase of the mass ratio of PTMD to structure. With the increase of base-isolation period, the hoop stress, axial compressive stress, effective stress and liquid pressure decrease, and the control effect of PTMD on the liquid storage tank is weakened.