It has been shown that the majority of existing adversarial defense methods achieve robustness at the cost of sacrificing prediction accuracy. The undesirable severe drop in accuracy adversely affects the reliability of machine learning algorithms and prohibits their deployment in realistic applications. This paper aims to address this dilemma by proposing a novel preprocessing framework, which we term Robust and Accurate Image classificatioN(RAIN), to improve the robustness of given CNN classifiers and, at the same time, preserve their high prediction accuracies. RAIN introduces a new randomization-enhancement scheme. It applies randomization over inputs to break the ties between the model forward prediction path and the backward gradient path, thus improving the model robustness. However, similar to existing preprocessing-based methods, the randomized process will degrade the prediction accuracy. To understand why this is the case, we compare the difference between original and processed images, and find it is the loss of high-frequency components in the input image that leads to accuracy drop of the classifier. Based on this finding, RAIN enhances the input's high-frequency details to retain the CNN's high prediction accuracy. Concretely, RAIN consists of two novel randomization modules: randomized small circular shift (RdmSCS) and randomized down-upsampling (RdmDU). The RdmDU module randomly downsamples the input image, and then the RdmSCS module circularly shifts the input image along a randomly chosen direction by a small but random number of pixels. Finally, the RdmDU module performs upsampling with a detail-enhancement model, such as deep super-resolution networks. We conduct extensive experiments on the STL10 and ImageNet datasets to verify the effectiveness of RAIN against various types of adversarial attacks.