The invention relates to a multi-connection and multi-span continuous steel truss girder bridge and a construction method thereof. The multi-connection and multi-span continuous steel truss girder bridge comprises a plurality of height-variable trusses, wherein the tail parts and head parts of the height-variable trusses are connected into a row, the upper part and lower part of each height-variable truss are respectively connected with an upper horizontal and longitudinal connection and a bridge surface, and the lower end of the bridge surface is fixedly connected with a plurality of bridge piers. The construction method comprises the following steps of preliminary work, building of the bridge piers, building of a top pushing splicing platform, jacking and pushing of the height-variable trusses, suspension and splicing of the height-variable trusses, paving of a worker walkway, cleaning of site, and completion. The multi-connection and multi-span continuous steel truss girder bridge and the construction method have the beneficial effects that the structure stress of the height-variable trusses is reasonable, and the steel consumption amount is reduced; by adopting the integral and splicing type node mixing structure, the splicing is simple; by adopting multiple main trusses, the transverse stress is reasonable; by arranging the worker walkway and a refuge platform in a gap between the main truss components, the truss width is effectively reduced, and the steel consumption amount is reduced; by adopting the multi-connection synchronous jacking, pushing, suspension and splicing combined construction method, the influence on the spliced jacking and pushing process of original connection caused by the new connection of splicing is avoided, the jacking and pushing quality is improved, the difficulty in synchronizing is decreased, the efficiency is improved, and the cost is reduced.