Remote sensing image dehazing is an extremely complex issue due to the irregular and non-uniform distribution of haze. In this paper, a prior-based dense attentive dehazing network (DADN) is proposed for single remote sensing image haze removal. The proposed network, which is constructed based on dense blocks and attention blocks, contains an encoder-decoder architecture, which enables it to directly learn the mapping between the input images and the corresponding haze-free image, without being dependent on the traditional atmospheric scattering model (ASM). To better handle non-uniform hazy remote sensing images, we propose to combine a haze density prior with deep learning, where an initial haze density map (HDM) is firstly extracted from the original hazy image, and is subsequently utilized as the input of the network, together with the original hazy image. Meanwhile, a large-scale hazy remote sensing dataset is created for training and testing of the proposed method, which contains both uniform and non-uniform, synthetic and real hazy remote sensing images. Experimental results on the created dataset illustrate that the developed dehazing method obtains significant progresses over the state-of-the-art methods.