To address the issue of frequent rear-end collisions on mountainous road sections, the risk of vehicle rear-end collisions on curved slope combination sections is assessed based on traffic conflict technology, and the influencing factors of rear-end collisions are identified. Vehicle trajectory and traffic flow data are collected through aerial photography by UAV (Unmanned aerial vehicle) and radar speed measurement. The traditional time to collision (TTC) calculation method has not fully considered the alignment characteristics of the curved slope combination section. According to the characteristics of road alignment and vehicle operation in each component (circle curve section, gentle curve section and straight curve section) of the curved slope combination road section, the vehicle rear-end collision time TTC is modified, and the classification thresholds of severe, moderate, slight and potential rear-end conflicts are 1.23 s, 2.59 s, 3.50 s and 4.0 s according to the cumulative distribution curve of conflict time. The tree structures for identifying the influence factors of rear-end conflicts on circular curve, gentle curve and straight curve road sections were constructed respectively, and the influence of each factor on the severity of rear-end conflicts was investigated by ordered logistic models. The results indicate that: the increase of traffic volume, the mixing of large vehicles, and the increase of vehicle travel speed and acceleration will promote the occurrence of conflicts as well as the severity of conflicts; There are differences in the effects of traffic flow characteristics indexes on rear-end conflicts in each road section; No significant differences in rear-end conflicts were found between vehicles approaching or exiting the direction of curves, and between inside and outside curves on circle sections; however, such differences existed on gently curved and straight sections. The results of this research help active safety prevention and control of rear-end collisions, as well as real-time forecasting to improve safety of travelling on curved road sections.