The invention discloses a geofoam backfill structure as well as a connecting piece and a construction method thereof. The structure comprises a pure soil layer, a coarse sand layer, a geofoam layer and surface-layer soil; the geofoam layer comprises multiple layers of stacked geofoam; first connecting pieces with L-shaped sections penetrate through the geofoam at the bottom layer; bottom ends of vertical rods of the first connecting pieces are inserted in the pure soil layer; second connecting pieces are arranged in positions of T-shaped seams of every three adjacent pieces of geofoam at the top layer; third connecting pieces are arranged at two ends of the upper surface of each piece of geofoam in the middle layer; each of the second connecting pieces and the third connecting pieces comprises a rectangular body, and two sides of the body extend outwards to form rectangular side plates; and triangular saw teeth inserted in the surfaces of the geofoam are arranged on peripheral edges of the side plates. The geofoam is light in mass, the problem of settlement can be well solved, the geofoam layer is compact in structure and high in integrity, the construction method is convenient to operate, the construction efficiency is high, and the structure can meet various terrain requirements.