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Adversarial training has been considered to be one of the most effective strategies to defend against adversarial attacks. Most existing adversarial training methods have shown a trade-off between training cost and robustness. This paper explores a new optimization direction from training data to reduce the computational cost of adversarial training without scarifying robustness. First, we show that some adversarial examples are less important, meaning that removing them does not hurt the robustness. Second, we propose a method to identify insignificant adversarial examples at a minimal cost. Third, we demonstrate that our approach can be integrated with other adversarial training frameworks with few modifications. The experimental results show that combined with previous works, our approach not only reduces about 20% of computational cost on the CIFAR10 and CIFAR100 datasets but also improves about 1.5% natural accuracy. With less computational cost, it achieves 58.22%, 30.68%, and 41.92% robust accuracy on CIFAR10, CIFAR100, and ImageNet datasets respectively, which are higher than those of the original methods. • Analyze the effectiveness of adversarial examples for adversarial training. • Design a method to remove inefficient adversarial examples but maintain the accuracy. • Design an algorithm to detect inefficient adversarial examples without extra cost. • Conduct experiments to demonstrate the compatibility with other frameworks. [ABSTRACT FROM AUTHOR]