The Hancock–Greenfield Bridge carries Forest Road (historically known as Old County Road) over the Contoocook River, which forms the border between eastern Hancock and northwestern Greenfield. It is a single-span Teco–Pratt timber truss, 88 feet (27 m) long and 27 feet 2 inches (8.28 m) wide, with an internal clearance of 14 feet (4.3 m). The road bed is 20 feet (6.1 m) wide and carries two lanes of traffic. The bridge's roof is sheathed in asphalt, and its walls are finished in vertical board siding. The vertical load-bearing trusses are joined by a latticework web at both the ceiling and floor, effectively making the structure into a single box truss. The roadway is asphalt laid on horizontally placed timbers. All of its major interconnection points are reinforced by steel gussets, and crossing and connection points of the trusses are made with steel pins.
The bridge was built in 1937, replacing a Long-truss covered bridge built in 1852. That structure was extensively damaged by flooding in 1936. The Timber Engineering Company of Washington, DC, provided the interconnecting elements, which greatly strengthen the structure, based on plans it had first published in 1935. Construction of these types of bridges was generally supplanted by the more economical steel girder bridges after World War II.