The segmentation of coronary arteries in X-ray images is essential for image-based guiding procedures and the diagnosis of cardiovascular disease. However, owing to the complex and thin structures of the coronary arteries, it is challenging to accurately segment arteries in X-ray images using only a single neural network model. Consequently, coronary artery images obtained by segmentation with a single model are often fragmented, with parts of the arteries missing. Sophisticated post-processing is then required to identify and reconnect the fragmented regions. In this paper, we propose a method to reconstruct the missing regions of coronary arteries using X-ray angiography images. Method: We apply an independent convolutional neural network model considering local details, as well as a local geometric prior, for reconnecting the disconnected fragments. We implemented and compared the proposed method with several convolutional neural networks with customized encoding backbones as baseline models. Results: When integrated with our method, existing models improved considerably in terms of similarity with ground truth, with a mean increase of 0.330 of the Dice similarity coefficient in local regions of disconnected arteries. The method is efficient and is able to recover missing fragments in a short number of iterations. Conclusion and Significance: Owing to the restoration of missing fragments of coronary arteries, the proposed method enables a significant enhancement of clinical impact. The method is general and can simply be integrated into other existing methods for coronary artery segmentation.