The vulnerability of neural networks under adversarial attacks has raised serious concerns and motivated extensive research. It has been shown that both neural networks and adversarial attacks against them can be sensitive to input transformations such as linear translation and rotation, and that human vision, which is robust against adversarial attacks, is invariant to natural input transformations. Based on these, this paper tests the hypothesis that model robustness can be further improved when it is adversarially trained against transformed attacks and transformation-invariant attacks. Experiments on MNIST, CIFAR-10, and restricted ImageNet show that while transformations of attacks alone do not affect robustness, transformation-invariant attacks can improve model robustness by 2.5\% on MNIST, 3.7\% on CIFAR-10, and 1.1\% on restricted ImageNet. We discuss the intuition behind this phenomenon.