Prostate cancer is one of the deadest cancers among human beings. To better diagnose the prostate cancer, prostate lesion segmentation becomes a very important work, but its progress is very slow due to the prostate lesions small in size, irregular in shape, and blurred in contour. Therefore, automatic prostate lesion segmentation from mp-MRI is a great significant work and a challenging task. However, the most existing multi-step segmentation methods based on voxel-level classification are time-consuming, may introduce errors in different steps and lead to error accumulation. To decrease the computation time, harness richer 3D spatial features, and fuse the multi-level contextual information of mp-MRI, we present an automatic segmentation method in which all steps are optimized conjointly as one step to form our end-to-end convolutional neural network. The proposed end-to-end network DMSA-V-Net consists of two parts: (1) a 3D V-Net is used as the backbone network, it is the first attempt in employing 3D convolutional neural network for CS prostate lesion segmentation, (2) a deep multi-scale attention mechanism is introduced into the 3D V-Net which can highly focus on the ROI while suppressing the redundant background. As a merit, the attention can adaptively re-align the context information between the feature maps at different scales and the saliency maps in high-levels. We performed experiments based on five cross-fold validation with data including 97 patients. The results show that the Dice and sensitivity are 0.7014 and 0.8652 respectively, which demonstrates that our segmentation approach is more significant and accurate compared to other methods.