Abstract: Passive safety systems are increasingly implemented in the design of advanced nuclear power plants, in order to improve the safety of reactors. Up to now, no systematic and mature methodology has been presented addressing the evaluation for passive thermal-hydraulic systems. Also its failure probability is generally not considered in PSA. This paper presents the quantification result of failure probability about natural circulation functional carried out for the Passive Residual Heat Removal System of Secondary Side（PRS） of PWR. The analysis took overall approach reported in the Reliability Methods for Passive System（RMPS, European Commission） project as reference. The importance indicators of parameters affecting its performances have been evaluated based on statistics methodology and T-H simulation. At last, natural circulation functional failure probability is calculated using Monte-Carlo method and also with Response Surface method. The assessment shows the functional failure probability of PRS is 2.14×10-3. The method adopted in this paper can be used in Passive safety systems design optimization.