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Mammography is one of the most commonly applied tools for early breast cancer screening. Automatic segmentation of breast masses in mammograms is essential but challenging due to the low signal-to-noise ratio and the wide variety of mass shapes and sizes. Existing methods deal with these challenges mainly by extracting mass-centered image patches manually or automatically. However, manual patch extraction is time-consuming and automatic patch extraction brings errors that could not be compensated in the following segmentation step. In this study, we propose a novel attention-guided dense-upsampling network (AUNet) for accurate breast mass segmentation in whole mammograms directly. In AUNet, we employ an asymmetrical encoder-decoder structure and propose an effective upsampling block, attention-guided dense-upsampling block (AU block). Especially, the AU block is designed to have three merits. Firstly, it compensates the information loss of bilinear upsampling by dense upsampling. Secondly, it designs a more effective method to fuse high- and low-level features. Thirdly, it includes a channel-attention function to highlight rich-information channels. We evaluated the proposed method on two publicly available datasets, CBIS-DDSM and INbreast. Compared to three state-of-the-art fully convolutional networks, AUNet achieved the best performances with an average Dice similarity coefficient of 81.8% for CBIS-DDSM and 79.1% for INbreast.