The accelerator-driven subcritical system (ADS) can transmute nuclear waste by using high-energy neutrons, which is the most effective nuclear waste disposal scheme at present. The zero-power lead-bismuth alloy device accurately constructed the interaction mode between nuclear fuel and lead-bismuth alloy coolant material, and more accurately simulated the core physical characteristics of lead-bismuth reactor. Moreover, the inherent safety of the reactor is enhanced by installing several passive safety shutdown systems. However, due to the particularity of the potential harm caused by radioactive material leakage, nuclear-grade equipment should maintain high safety performance under many working conditions, such as earthquake working conditions. To ensure the safe operation of the ADS zero-power device and the safe shutdown under seismic conditions, the motion of the control rod of the ADS zero-power device must be analyzed under seismic conditions. At present, most studies on the control rod drop analysis focus on water reactor, but this paper will analyze and calculate the control rod drop of the lead reactor. In this paper, the physical mechanism of rod falling of the control rod component is analyzed, and the influence of contact collision between the control rod component and the guide tube of the control rod on the whole rod falling time is considered. In this paper, the finite element method is used for transient analysis of ADS lead-bismuth alloy zero power reactor, and the time history diagram of the control bar position is obtained under the seismic conditions, thus verifying that ADS lead-bismuth alloy zero power reactor can be safely shut down under the safe shutdown earthquake (SSE).