The earthquake-explosion sequence is one of the typical multi-hazard coupling scenarios in chemical industrial parks (CIPs), of which hazardous installation units are easily damaged by the combined loadings. However, the structural dynamic responses behavior is extremely complex and associated with non-stationary relations. It is still challenging to capture a clear insight into the structural failure caused by sequential multi-hazards. This work focuses on the damage amplified phenomena of the steel cylindrical tank under the earthquake-explosion sequence. Specifically, a consecutive coupling approach is established, considering the interaction between the tank and stored liquid. The coupling effects of earthquake loading and blast wave on the deformation characteristics, stress response, energy absorption, and anti-blasting ability of the tank are investigated. Additionally, the effects of the seismic intensity and explosion intensity are analyzed. The results indicate that the failure of the tank probably appears in the upper portion under combined loadings. Compared to the tank without earthquake action, the seismic damage status results in multiple stress concentrations. The dynamic responses of the seismic damage tank under explosions are higher, which are 1.0–2.4 times than the case without earthquake action. Moreover, with the explosion intensity decreasing, the damage amplification effect of the tank under combined loadings becomes more apparent. Negative pressure and the impact of convective pressure formed by the liquid sloshing are the main factors causing the depression deformation of tank structure under the coupling effect. With the plastic deformation of the tank caused by earthquakes, the anti-blast performance of the tank will further reduce. The coupling scenarios of bi-directional earthquakes will cause more severe consequences than the uni-directional earthquake, while there are no significant differences in the coupling amplification effects in this work. These conclusions contribute to exploring the complex failure mechanisms of the tank exposed to post-earthquake explosion scenarios.