In response to the inaccurate probability characteristics of the corrosion degradation process of in-service stay cables, this study utilizes the probability box (p-box) theory to establish the interval probability model of stay cable corrosion failure and investigates the influence of cognitive uncertainty of parameters on the failure probability of stay cables. Numerical analysis results show that after the cognitive uncertainty of parameters is considered, the gap between the upper and lower bounds of the failure probability interval of stay cables is highly distinct, and the failure probability interval progressively widens with time. In a non-marine environment, the failure probability of stay cables has the highest sensitivity to rust diffusion ratio r. The more the uncertain parameters considered, the greater the cognitive uncertainty involved, and the wider the failure probability interval of stay cables. At the same time, the improvement of the confidence level also significantly increases the failure probability interval of stay cables. To improve the credibility of each confidence level, more data of uncertain parameters need to be collected.