The idling behavior of the reactor coolant pump is referred to as an important indicator of the safe operation of the nuclear power system, while the idling transition process under the power failure accident condition is developed as a transient flow process. In this process, the parameters such as the flow rate, speed, and head of the reactor coolant pump are all nonlinear changes. In order to ensure the optimal idling behavior of the reactor coolant pump under the power cutoff accident condition, this manuscript takes the guide vanes of the AP1000 reactor coolant pump as the subject of this study. In this paper, the mathematical model of idling speed and flow characteristic curve of reactor coolant pump under the power failure condition were proposed, while the hydraulic modeling database of different vane structure parameters was modeled based on the orthogonal optimization schemes. Furthermore, based on the mathematical modeling framework of multiple linear regressions, the mathematical relationship of the hydraulic performance of each guide vane in different parameters was predicted. The derived model was verified with the idling test data.