In order to improve the transverse alignment accuracy of the control network in Chinese Spallation Neutron Source (CSNS) Linac, a 200-m stretched wire-based system was established in the tunnel. A wire position sensor based on bi-telecentric technology (tWPS) was specially designed to obtain the offset with respect to the stretched wire. A control network adjustment algorithm with additional wire constraints has been developed. The laser tracker measured station by station in a free station way, and measured the control network and the fiducials of the tWPS at the same time. The offset observation equation was combined with the angle observation equation and distance observation equation of the laser tracker for joint solution. As a result, the transverse accuracy of the control network was improved from 0.061 mm without wire constraint to 0.028 mm with wire constraint, which indicates that the addition of wire constraints can indeed effectively improve the transverse accuracy of the longitudinal control network.