The Fenshui River Bridge is a steel–concrete composite girder bridge with a main span of 90 m. Due to the topographical constraints, the steel box girder was constructed without the use of auxiliary piers, employing incremental launching techniques. This article focuses on the construction technology used for the steel box girder of the Fenshui River Bridge. Firstly, using the influence matrix method, the cable force is determined based on the maximum cantilever state of the structure, with the vertical deformation of the front end of the guide beam and the horizontal deformation of the top of the tower as the control objectives. The unstressed cable length is then calculated based on the mechanical relationship between cable deformation and cable force. A calculation method for adaptive cable force is proposed, which is based on the variation of the stress-free cable length within the adaptive structural system. Next, the finite element analysis method was employed to determine the optimal layout position for the tower. The results indicate that during the incremental launching construction of the steel box girder, the calculated cable forces using the method proposed in this paper are in close agreement with the measured cable forces. At the maximum cantilever state of the structure, the calculated and measured values of the cable force resulted in a percentage difference of 3.96%. The calculated values of deformation and stress in key sections showed a percentage difference of 6.4% for deformation and 6.6% for stress. To maximize the effectiveness of the tower and cable, the tower should be positioned above the bridge pier when the guide beam crosses the maximum span. The findings of this paper can serve as a reference for the construction of similar types of bridges.