The safety of nuclear power plants (NPPs) under earthquake is of great significance to the development of nuclear energy. In order to study the influence of structural parameter uncertainty on random seismic response of NPP, a random response analysis method considering structural parameter uncertainty is proposed based on cubature formula; using the random vibration theory, the expression of response power spectrum considering structural parameters is derived. And this proposed method is verified by a single degree of freedom model. The results show that considering the uncertainty of structural parameters has a great impact on the response power spectrum. the power spectrum value of structural response is more dispersed in the frequency range due to the randomness of its parameters. The root means square of response obtained by cubature formula is closer to the results of Monte Carlo simulation (MCS) and is larger than the results without considering the parameter uncertainty. The finite element model of an NPP is established, and the random seismic response considering the uncertain material parameters of the NPP structure is calculated based on the cubature formula. The results show that the maximum response of the structure will be underestimated and the reliability of the structure will be overestimated without considering the uncertainty of structural parameters. Therefore, this method can be used to consider the uncertainty of parameter of important structures in practical engineering.