Vessel centerline extraction is essential for carotid stenosis assessment and atherosclerotic plaque identification in clinical diagnosis. Simultaneously, it provides a region of interest identification and boundary initialization for computer-assisted diagnosis tools. In magnetic resonance imaging (MRI) cross-sectional images, the lumen shape and vascular topology result in a challenging task to extract the centerline accurately. To this end, we propose a space-refine framework, which exploits the positional continuity of the carotid artery from frame to frame to extract the carotid artery centerline. The proposed framework consists of a detector and a refinement module. Specifically, the detector roughly extracts the carotid lumen region from the original image. Then, we introduce a refinement module that uses the cascade of regressors from a detector to perform sequence realignment of lumen bounding boxes for each subject. It improves the lumen localization results and further enhances the centerline extraction accuracy. Verified by large carotid artery data, the proposed framework achieves state-of-the-art performance compared to conventional vessel centerline extraction methods or standard convolutional neural network approaches.Clinical relevance- Our proposed framework can be used as an important aid for physicians to quantitatively analyze the carotid artery in clinical practice. It is also used as a new paradigm for extracting the centerline of carotid vessels in computer-assisted tools.