Considering the uncertainties of the stochastic parameters of an inter-story isolation system and seismic excitation, the implicit structural response function is transformed into an explicit one by SRSM (Stochastic Response Surface Method), combined with the probabilistic collocation method based on the linear independence principle. Then, the reliability and sensitivity of the structure are analyzed using the Monte-Carlo. The results show that the change of each stochastic variant average has different effects on system reliability, which is reduced as the variance of each variant increases. Optimizing design variables and controlling construction quality are important in reducing their impact on the system′s reliability. The analysis results of the reliability sensitivity can provide system reliability indexes to rank stochastic parameters by importance, in order to improve the efficiency of the large-scale complex structure reliability analysis and optimization design. The results also lay the foundation for further study of the reliability sensitivity of the inter-story isolation system.