This article investigates the issue of beam misalignment in continuous curved beam bridges. Taking the D0–D6 spans of the Gongbin Road elevated bridge as a basis, real-time monitoring of the stress and displacement of the beams is carried out during the jacking and shifting construction process. At the same time, the reaction forces of each support are monitored. The jacking force of the hydraulic jacks is controlled to ensure the stability and safety of the beam during the construction process. Finally, the jacking and shifting monitoring data is organized and compared with theoretical values. It is found that the stress values generated during the jacking phase of the bridge are below the stress control standard. No uplift phenomenon occurs at the supports, and the jacking height is controlled within a reasonable range. The construction process does not cause damage to the beams, and it is safe and reliable. During the shifting construction, the whole bridge was displaced using the jacking method, and the three working conditions were monitored throughout the process. The stress increment at the 2# and 4# sections was relatively small, and the measured stress increments for the entire bridge were all below the stress control standard. The displacement of the bridge abutment during the jacking process was minimal, with no contact with the abutment blocks, and no significant elastic deformation occurred. The jacking displacement was successfully achieved.