In a rigid connection structure of a bridge pier and concrete girder, a joint-equipped PC concrete girder is constituted by burying a rear half part of a shaped-steel joint formed of short shaped-steel respectively in both ends of the concrete girder and protruding a front half part of each shaped-steel joint respectively from each end face of the concrete girder, the respective shaped-steel joint portions protruded from the respective end faces of the concrete girders are supported on a bridge abutment face of a bridge pier while being connected to a connection strip member which arises from the bridge abutment face, and the respective shaped-steel joint portions and the connection strip member are buried in connection concrete which is additionally casted on the bridge abutment face.