Cable-stayed bridges, due to their unique mechanical structure, have the ability to span larger distances, therefore, they are increasingly emphasized in modern bridge construction. With the continuous im-provement of engineering requirements, cable-stayed bridges have gradually become a primary bridge type for long-span structures. Due to the complexity of cable-stayed bridge structures, to ensure that the actual construction state of the bridge is close to optimal, the bridge must be strictly monitored and con-trolled during construction. In this paper, Jinwu Bridge in Jinhua, Zhejiang Province, is taken as the research background. This bridge is an asymmetric single-tower cable-stayed bridge. The spans and materials of the main girders on both sides of the bridge pylons are different. During the tensioning of stay cables, the space effect of the main girder is prone to generating an unbalanced moment. Herein, a study on the tensioning scheme of stay cables is carried out. The results show that, compared with those of the one-time tensioning scheme for stay cables, the stress state and cable force of the bridge are better when the two-time tensioning scheme is used, meeting the construction monitoring requirements.