Adversarial robustness describes the ability of the model to resist adversarial examples and adversarial training is a common method to improve the model's adversarial robustness. However, adversarial training will reduce the accuracy of the model on clean samples. This phenomenon is called accuracy-robustness problem. Due to the need to generate adversarial examples during the adversarial training, this process significantly increases the training time of the network. This work studies the relationship between prediction uncertainty and adversarial robustness, and draws the following conclusions: the greater the prediction uncertainty, the greater the adversarial robustness. The conclusion is explained as: the boundary of the model obtained by cross-entropy is not perfect. In order to minimize the cross-entropy, the classification surface of some classes may become narrow, which makes the samples of these classes vulnerable to adversarial attacks. And if the output's information entropy is maximized while training the model, the classification surface of the model could be more balanced, that is, the distance between boundary and data is as far as possible, which makes it more difficult for the attacker to attack the samples. Based on this finding, a new methodis proposed to improve the adversarial robustness of the model, by increasing the uncertainty of the model's prediction to improve the adversarial robustness of the model. While ensuring the accuracy of the model, the prediction's information entropy is larger. Extensive experiments and simplified model derivations on the MNIST, CIFAR-10, and CIFAR-100 datasets have confirmed the statistical relationship that the adversarial robustness increases with the increase of the model's prediction uncertainty. The method proposed in this study also can be combined with adversarial training to further improve the model's adversarial robustness.