Deep convolutional neural networks (CNNs) are often of sophisticated design with numerous learnable parameters for the accuracy reason. To alleviate the expensive costs of deploying them on mobile devices, recent works have made huge efforts for excavating redundancy in pre-defined architectures. Nevertheless, the redundancy on the input resolution of modern CNNs has not been fully investigated, i.e., the resolution of input image is fixed. In this paper, we observe that the smallest resolution for accurately predicting the given image is different using the same neural network. To this end, we propose a novel dynamic-resolution network (DRNet) in which the input resolution is determined dynamically based on each input sample. Wherein, a resolution predictor with negligible computational costs is explored and optimized jointly with the desired network. Specifically, the predictor learns the smallest resolution that can retain and even exceed the original recognition accuracy for each image. During the inference, each input image will be resized to its predicted resolution for minimizing the overall computation burden. We then conduct extensive experiments on several benchmark networks and datasets. The results show that our DRNet can be embedded in any off-the-shelf network architecture to obtain a considerable reduction in computational complexity. For instance, DR-ResNet-50 achieves similar performance with an about 34% computation reduction, while gaining 1.4% accuracy increase with 10% computation reduction compared to the original ResNet-50 on ImageNet. Code will be available at https://gitee.com/mindspore/models/tree/master/research/cv/DRNet.