Coronary artery segmentation has great significance in providing morphological information and treatment guidance in clinics. However, the complex structures with tiny and narrow branches of the coronary artery bring it a great challenge. Limited by the low resolution and poor contrast of medical images, voxel-based segmentation methods could potentially lead to fragmentations of segmented vessels and surface voids are commonly found in the reconstructed mesh. Therefore, we propose a geometry-based end-to-end segmentation method for the coronary artery in computed tomography angiography. A U-shaped network is applied to extract image features, which are projected to mesh space, driving the geometry-based network to deform the mesh. Integrating the ability of geometric deformation, the proposed network could output mesh results of the coronary artery directly. Besides, the centerline-based approach is utilized to produce the ground truth of the mesh instead of the traditional marching cube method. Extensive experiments on our collected dataset CCA-520 demonstrate the feasibility and robustness of our method. Quantitatively, our model achieves Dice of 0.779 and HD of 0.299, exceeding other methods in our dataset. Especially, our geometry-based model generates an accurate, intact and smooth mesh of the coronary artery, devoid of any fragmentations of segmented vessels.