Adversarial training (AT) aims to improve the robustness of deep learning models by mixing clean data and adversarial examples (AEs). Most existing AT approaches can be grouped into restricted and unrestricted approaches. Restricted AT requires a prescribed uniform budget to constrain the magnitude of the AE perturbations during training, with the obtained results showing high sensitivity to the budget. On the other hand, unrestricted AT uses unconstrained AEs, resulting in the use of AEs located beyond the decision boundary; these overestimated AEs significantly lower the accuracy on clean data. These limitations mean that the existing AT approaches have difficulty in obtaining a comprehensively robust model with high accuracy and robustness when confronting attacks with varying strengths. Considering this problem, this paper proposes a novel AT approach named blind adversarial training (BAT) to better balance the accuracy and robustness. The main idea of this approach is to use a cutoff-scale strategy to adaptively estimate a nonuniform budget to modify the AEs used in the training, ensuring that the strengths of the AEs are dynamically located in a reasonable range and ultimately improving the overall robustness of the AT model. The experimental results obtained using BAT for training classification models on several benchmarks demonstrate the competitive performance of this method.