Abstract: Functional failure becomes an important factor in the natural circulation system operation failure, which needs to be considered in the system reliability analysis. In order to solve the problem of multi-dimensional uncertainty parameters and small functional failure probability of passive system, an efficient functional reliability estimation method based on improved response surface and importance sampling subset simulation methods was presented. This method was applied in natural circulation cooling in Xi’an Pulsed Reactor (XAPR) core. Combined with MLOCA, the uncertainties related to the input parameters and the model were considered. And then the probability of functional failure and the sensitivity measures were estimated. The assessment results show that the functional failure probability of natural circulation for XAPR core is 3.796×10^-3, and the functional failure in the passive system reliability analysis should be fully considered. This method has high computed efficiency and excellent computed accuracy compared with traditional probability analysis methods, and it is robust to nonlinear functional function of natural circulation for XAPR core.