The invention provides a support device for constructing a continuous box girder bridge and an elevation adjusting method. The continuous box girder bridge comprises an upper structure and a bridge pier bearing platform for bearing the upper structure; the upper structure on the sidespan of the continuous box girder bridge is provided with a concrete cast-in-place box girder; the support device supports the concrete cast-in-place box girder, and takes the bridge pier bearing platform of the constructed continuous box girder bridge as a stance of a steel tube holder in the support device to support the concrete cast-in-place box girder, and the safety of the cast-in-place section of the concrete box girder is ensured in the cast-in-place process; and the elevation adjusting method comprises a step of applying pre-jacking force on the concrete cast-in-place box girder through a jack to adjust the elevation of the concrete cast-in-place box girder, so that the control and adjustment of the altitude difference of the sidespan closure of prestressed concrete are facilitated.