Cardiovascular diseases (CVD), as the leading cause of death in the world, poses a serious threat to human health. The segmentation of carotid Lumen-intima interface (LII) and Media-adventitia interface (MAI) is a prerequisite for measuring intima-media thickness (IMT), which is of great significance for early screening and prevention of CVD. Despite recent advances, existing methods still fail to incorporate task-related clinical domain knowledge and require complex post-processing steps to obtain fine contours of LII and MAI. In this paper, a nested attention-guided deep learning model (named NAG-Net) is proposed for accurate segmentation of LII and MAI. The NAG-Net consists of two nested sub-networks, the Intima-Media Region Segmentation Network (IMRSN) and the LII and MAI Segmentation Network (LII-MAISN). It innovatively incorporates task-related clinical domain knowledge through the visual attention map generated by IMRSN, enabling LII-MAISN to focus more on the clinician's visual focus region under the same task during segmentation. Moreover, the segmentation results can directly obtain fine contours of LII and MAI through simple refinement without complicated post-processing steps. To further improve the feature extraction ability of the model and reduce the impact of data scarcity, the strategy of transfer learning is also adopted to apply the pretrained weights of VGG-16. In addition, a channel attention-based encoder feature fusion block (EFFB-ATT) is specially designed to achieve efficient representation of useful features extracted by two parallel encoders in LII-MAISN. Extensive experimental results have demonstrated that our proposed NAG-Net outperformed other state-of-the-art methods and achieved the highest performance on all evaluation metrics.