We are developing an automated registration method for coronary arterial trees from multiple-phase cCTA to build a best-quality tree to facilitate detection of stenotic plaques. Cubic B-spline with fast localized optimization (CBSO) is designed to register the initially segmented left and right coronary arterial trees (LCA or RCA) separately in adjacent phase pairs where displacements are small. First, the corresponding trees in phase 1 and 2 are registered. The phase 3 tree is then registered to the combined tree. Similarly the trees in phases 4, 5, and 6 are registered. An affine transform with quadratic terms and nonlinear simplex optimization (AQSO) is designed to register the trees between phases with large displacements, namely, registering the combined tree from phases 1, 2, and 3 to that from phases 4, 5, and 6. Finally, CBSO is again applied to the AQSO registered volumes for final refinement. The costs determined by the distances between the vessel centerlines, bifurcation points and voxels of the trees are minimized to guide both CBSO and AQSO registration. The registration performance was evaluated on 22 LCA and 22 RCA trees on 22 CTA scans with 6 phases from 22 patients. The average distance between the centerlines of the registered trees was used as a registration quality index. The average distances for LCA and RCA registration for 6 phases and 22 patients were 1.49 and 1.43 pixels, respectively. This study demonstrates the feasibility of using automated method for registration of coronary arterial trees from multiple cCTA phases.