The invention relates to a seismic-resistant integral abutment bridge with energy absorption materials embedded in pier tops and a construction method of the seismic-resistant integral abutment bridge. The seismic-resistant integral abutment bridge comprises abutments, one sides of the abutments close to the earth are connected with connecting plates, the other ends of the connecting plates are connected with behind-abutment lapping plates, the connecting plates and the abutments are cast integrally, support piers are arranged below the abutments, miniature piers are arranged below the behind-abutment lapping plates and the connecting plates, the direction of the pier length or the long shaft of the support piers and the miniature piers is perpendicular to the longitudinal deformation direction of the bridge, and the energy absorption materials are filled between the tops of the support piers and the miniature piers and the surrounding earth, and the section of the energy absorption materials is identical with that of the piers. The seismic-resistant integral abutment bridge is simple in structure and reasonable in stress, the body damage of the support piers and the miniature piers is alleviated, and the seismic-resistant integral abutment bridge is high in longitudinal deformation and good in seismic resistance.