Whenever a visual scene is cast onto the retina, much of it will appear degraded due to poor resolution in the periphery; moreover, optical defocus can cause blur in central vision. However, the pervasiveness of blurry or degraded input is typically overlooked in the training of convolutional neural networks (CNNs). We hypothesized that the absence of blurry training inputs may cause CNNs to rely excessively on high spatial frequency information for object recognition, thereby causing systematic deviations from biological vision. We evaluated this hypothesis by comparing standard CNNs with CNNs trained on a combination of clear and blurry images. We show that blur-trained CNNs outperform standard CNNs at predicting neural responses to objects across a variety of viewing conditions. Moreover, blur-trained CNNs acquire increased sensitivity to shape information and greater robustness to multiple forms of visual noise, leading to improved correspondence with human perception. Our results provide multi-faceted neurocomputational evidence that blurry visual experiences may be critical for conferring robustness to biological visual systems.