The invention discloses a culvert structure adopting high density polyethylene (HDPE) winding reinforcement pipes and foam concrete. The culvert structure comprises a culvert pipe foundation, culvert pipes and filling bodies located on the two sides and the upper portions of the culvert pipes. The filling bodies are foam concrete filling bodies. The culvert pipes comprise the multiple HDPE winding reinforcement pipes which are connected in an end-to-end mode in sequence. The inner side of the connecting position of every two adjacent HDPE winding reinforcement pipes is provided with an annular steel band in a winding mode. Seepage-proofing sealing structures are disposed between the annular steel bands and the HDPE winding reinforcement pipes. Sealing reinforcement devices are disposed on the annular steel bands. The culvert structure is small in self weight, low in requirement for foundation bearing capacity, capable of effectively solving the problems of differential settlement and cambering of the culvert pipes and suitable for the environment conditions of corrosion and abrasion. The invention discloses a construction method of the culvert structure. The construction method includes the steps of (1) culvert pipe foundation construction, (2) culvert pipe mounting, (3) construction of the filling bodies and (4) construction of a road surface. By means of the construction method, the foam concrete is used as a filling material, and the link of compacting the fillers on the arch apex and culvert sides is omitted.