Multispectral remote sensing (RS) images are often contaminated by the haze that degrades the quality of RS data and reduces the accuracy of interpretation and classification. Recently, the emerging deep convolutional neural networks (CNNs) provide us new approaches for RS image dehazing. Unfortunately, the power of CNNs is limited by the lack of sufficient hazy-clean pairs of RS imagery, which makes supervised learning impractical. To meet the data hunger of supervised CNNs, we propose a novel haze synthesis method to generate realistic hazy multispectral images by modeling the wavelength-dependent and spatial-varying characteristics of haze in RS images. The proposed haze synthesis method not only alleviates the lack of realistic training pairs in multispectral RS image dehazing but also provides a benchmark data set for quantitative evaluation. Furthermore, we propose an end-to-end RSDehazeNet for haze removal. We utilize both local and global residual learning strategies in RSDehazeNet for fast convergence with superior performance. Channel attention modules are incorporated to exploit strong channel correlation in multispectral RS images. Experimental results show that the proposed network outperforms the state-of-the-art methods for synthetic data and real Landsat-8 OLI multispectral RS images.