Biomedical image segmentation has been widely studied, and lots of methods have been proposed. Among these methods, attention U-Net has achieved a promising performance. However, it has drawbacks of extracting the multi-scaled receptive field features at the high-level feature maps, resulting in the degeneration when dealing with the lesions with apparent scale variations. To solve this problem, this paper integrates an atrous spatial pyramid pooling (ASPP) module in the contracting path of attention U-Net. This module employs multiple dilation rates for the purpose of obtaining several multi-scale receptive fields, which significantly improves the networks' ability of handling both large and small lesions. Evaluation experimental result shows that our approach significantly improves the performance of medical image segmentation and substantially outperforms the representative deep learning models on public datasets.