Single image dehazing has been a challenging problem which aims to recover clear images from hazy ones. The performance of existing image dehazing methods is limited by hand-designed features and priors. In this paper, we propose a multi-scale deep neural network for single image dehazing by learning the mapping between hazy images and their transmission maps. The proposed algorithm consists of a coarse-scale net which predicts a holistic transmission map based on the entire image, and a fine-scale net which refines dehazed results locally. To train the multi-scale deep network, we synthesize a dataset comprised of hazy images and corresponding transmission maps based on the NYU Depth dataset. In addition, we propose a holistic edge guided network to refine edges of the estimated transmission map. Extensive experiments demonstrate that the proposed algorithm performs favorably against the state-of-the-art methods on both synthetic and real-world images in terms of quality and speed.