This paper studies the challenging black-box adversarial attack that aims to generate adversarial examples against a black-box model by only using output feedback of the model to input queries. Some previous methods improve the query efficiency by incorporating the gradient of a surrogate white-box model into query-based attacks due to the adversarial transferability. However, the localized gradient is not informative enough, making these methods still query-intensive. In this paper, we propose a Prior-guided Bayesian Optimization (P-BO) algorithm that leverages the surrogate model as a global function prior in black-box adversarial attacks. As the surrogate model contains rich prior information of the black-box one, P-BO models the attack objective with a Gaussian process whose mean function is initialized as the surrogate model's loss. Our theoretical analysis on the regret bound indicates that the performance of P-BO may be affected by a bad prior. Therefore, we further propose an adaptive integration strategy to automatically adjust a coefficient on the function prior by minimizing the regret bound. Extensive experiments on image classifiers and large vision-language models demonstrate the superiority of the proposed algorithm in reducing queries and improving attack success rates compared with the state-of-the-art black-box attacks.