The lead–bismuth fast reactor is a type of Generation IV reactor, in which the primary loop is typically cooled by natural circulation. One of the critical stages in conducting a passive reliability safety analysis is the selection of key parameters for the natural circulation cooling process in the primary loop of a lead–bismuth fast reactor. In order to resolve this matter, this paper implements the Analytic Hierarchy Process (AHP) to identify critical parameters that are present in the primary loop’s natural circulation cooling process in a lead–bismuth fast reactor, analyze the causal relationships among factors within the natural circulation cooling system of the primary loop in a lead–bismuth fast reactor. Establish a multi-level hierarchical structure model, using pairwise comparison and ranking methods to construct a judgment matrix and calculate the relative weights of each related element. After performing a consistency check on the judgment matrix, the synthetic weights of elements at each level with respect to the system objective are computed, ranked in descending order, and used to identify and prioritize the key factors impacting the natural circulation cooling system in the primary loop. This paper applies the above methodology to a case study, and through analysis, it is found that in the natural circulation cooling system of the primary loop in a lead–bismuth fast reactor, the key ranking of parameters such as lead–bismuth alloy flow rate, inlet temperature, pressure in the riser section of the test loop, heating power, and cooling water inlet temperature and so on are identified. These results provide fundamental reliability parameters for probabilistic safety analysis and real-time probabilistic risk assessment of the natural circulation cooling process in the primary loop of the lead–bismuth fast reactor.