The invention relates to a bridge girder erection machine capable of passing through a tunnel and realizing girder erection and a bridging process thereof. The bridge girder erection machine comprises a mainframe and a lower guide beam, the mainframe comprises a main beam, and also comprises a rear ground jack, a rear guide beam overhead travelling crane, a rear crane trolley, a front crane trolley, a front ground jack, an auxiliary travelling ground jack and a front guide beam overhead travelling crane which are arranged successively from the rear end to the front end of the main beam; a track is arranged on the main beam, and the front crane trolley, the rear crane trolley, the front guide beam overhead travelling crane and the rear guide beam overhead travelling crane run on the track;the lower guide beam comprises a main beam of the lower guide beam, a rear ground jack arranged behind the lower part of the main beam, and a front ground jack arranged in front of the lower part of the main beam; the bridge girder erection machine and the bridging process can realize bridge girder erection and beam erection operations in mountain areas; a mode of mixed beam taking by the crane trolleys of the bridge girder erection machine, a beam transporting vehicle and a pack trolley can realize beam erection at a tunnel portal; and when passing a tunnel, a plurality of components can be retracted and folded to enable the bridge girder erection machine to pass through the channel conveniently without being limited by the diameter of the tunnel, and the bridging construction efficiencyis high and the bridging operation is stable.