The accurate segmentation of multiple types of lesions from adjacent tissues in medical images is significant in clinical practice. Convolutional neural networks (CNNs) based on the coarse-to-fine strategy have been widely used in this field. However, multi-lesion segmentation remains to be challenging due to the uncertainty in size, contrast, and high interclass similarity of tissues. In addition, the commonly adopted cascaded strategy is rather demanding in terms of hardware, which limits the potential of clinical deployment. To address the problems above, we propose a novel Prior Attention Network (PANet) that follows the coarse-to-fine strategy to perform multi-lesion segmentation in medical images. The proposed network achieves the two steps of segmentation in a single network by inserting a lesion-related spatial attention mechanism in the network. Further, we also propose the intermediate supervision strategy for generating lesion-related attention to acquire the regions of interest (ROIs), which accelerates the convergence and obviously improves the segmentation performance. We have investigated the proposed segmentation framework in two applications: 2D segmentation of multiple lung infections in lung CT slices and 3D segmentation of multiple lesions in brain MRIs. Experimental results show that in both 2D and 3D segmentation tasks our proposed network achieves better performance with less computational cost compared with cascaded networks. The proposed network can be regarded as a universal solution to multi-lesion segmentation in both 2D and 3D tasks. The source code is available at https://github.com/hsiangyuzhao/PANet.