Background and objective: The vessel segmentation in CT angiography (CTA) provides an important basis for automatic diagnosis and hemodynamics analysis. Virtual unenhanced (VU) CT images obtained by dual-energy CT can assist clinical diagnosis and reduce radiation dose by obviating true unenhanced imaging (UECT). However, accurate segmentation of all vessels in the head-neck CTA (HNCTA) remains a challenge, and VU images are currently not available from conventional single-energy CT imaging. Methods:In this paper, we proposed a self-supervised dual-task deep learning strategy to fully automatically segment all vessels and predict unenhanced CT images from single-energy HNCTA based on a developed iterative residual-sharing scheme. The underlying idea was to use the correlation between the two tasks to improve task performance while avoiding manual annotation for model training. Results: The feasibility of the strategy was verified using the data of 24 patients. For vessel segmentation task, the proposed model achieves a significantly higher average Dice coefficient (84.83%, P-values 10−3 in paired t-test) than the state-of-the-art segmentation model, vanilla VNet (78.94%), and several popular 3D vessel segmentation models, including Hessian-matrix based filter (62.59%), optically-oriented flux (66.33%), spherical flux model (66.91%), and deep vessel net (66.47%). For the unenhanced prediction task, the average ROI-based error compared to the UECT in the artery tissue is 6.1±4.5 HU, similar to previously reported 6.4±5.1 HU for VU reconstruction. Conclusions: Results show that the proposed dual-task framework can effectively improve the accuracy of vessel segmentation in HNCTA, and it is feasible to predict the unenhanced image from single-energy CTA, providing a potential new approach for radiation dose saving. Moreover, to our best knowledge, this is the first reported annotation-free deep learning-based full-image vessel segmentation for HNCTA.