Hazy images are common in real scenarios and many dehazing methods have been developed to automatically remove the haze from images. Typically, the goal of image dehazing is to produce clearer images from which human vision can better identify the object and structural details present in the images. When the ground-truth haze-free image is available for a hazy image, quantitative evaluation of image dehazing is usually based on objective metrics, such as Peak Signal-to-Noise Ratio (PSNR) and Structural Similarity (SSIM). However, in many applications, large-scale images are collected not for visual examination by human. Instead, they are used for many high-level vision tasks, such as automatic classification, recognition and categorization. One fundamental problem here is whether various dehazing methods can produce clearer images that can help improve the performance of the high-level tasks. In this paper, we empirically study this problem in the important task of image classification by using both synthetic and real hazy image datasets. From the experimental results, we find that the existing image-dehazing methods cannot improve much the image-classification performance and sometimes even reduce the image-classification performance.