Single-vehicle accidents often occur in time periods with low traffic volume and poor road conditions, and their fatality rate is significantly higher than the average mortality rate of traffic accidents. To explore the key factors affecting the accident severity degree of single-vehicle accidents, based on the single-vehicle traffic accident data from 2015 to 2019 in some regions of China, this paper selected 24 accident-influencing factors from aspects such as people, vehicles, roads, and the environment. The temporal stability of the accident data was tested by the log-likelihood ratio test which found that there was temporal instability in the accident data, so it should be divided into five years for separate modeling. Then, a random parameter Logit model considering the mean-variance heterogeneity was constructed. The marginal effects of accident factor variables were compared. The results show that the temporal stability models of the five different years all have good fitting effects. The model can effectively capture the unobserved heterogeneity, and the captured parameters under different time models also exhibit randomness. The results of model parameter estimation indicate that four accident factors, namely the type of intersection and road section, passenger cars, motorcycles, and accident liability, have temporal stability, while other accident-influencing factors only have significant effects in individual years. The accident factor of protective facilities also have temporal stability. Accident factor variables such as passenger cars, motorcycles, the state of vehicle headlights, vehicle safety conditions, hitting fixed objects, and accident liability will significantly increase the possibility of casualties in single-vehicle accidents. Variables such as the type of protective facilities and visibility greater than 100 meters will significantly reduce the severity of injuries.