The invention discloses a single girder type guide beam-free bridge erection machine which comprises a box girder, a front landing leg and a rear landing leg, wherein the front landing leg is arranged under the front part of the box girder and is stretchable; the rear landing leg further comprises a first horizontal beam, two inclined beams, two vertical beams and two second horizontal beams; the first horizontal beam is located on an erected deck under the rear part of the box girder; the two inclined beams are respectively connected with the two ends of the first horizontal beam; one end of each of the two vertical beams is connected with each of the inclined beams; the other ends of the two vertical beams are connected with each other; the second horizontal beams are connected with the side wall of the box girder. The invention also provides a spanning method and a low-position tunnel-crossing method for the single girder type guide beam-free bridge erection machine. The single girder type guide beam-free bridge erection machine can be used for solving the technical problems that the bridge erection machine crosses a small-radius tunnel and is used for erecting the bridge in a short distance at the tunnel entrance. The single girder type guide beam-free bridge erection machine has the advantages of simple structure, light weight, no anchoring requirement and capability of greatly increasing the construction efficiency and the safety performance.