The invention relates to a rubber-tired track-laying crane and a construction method thereof, belongs to the field of engineering construction equipment, and especially relates to a multi-leg rubber-tired track-laying crane and a construction method thereof. The multi-leg rubber-tired track-laying crane comprises a main beam, telescopic legs and a wheel set, wherein the wheel set is mounted on the main beam through the telescopic legs. The structure of the crane is characterized in that the wheel set comprises wheel-set legs and a balance beam, wherein the upper parts of the wheel-set legs are connected to the telescopic legs and the lower parts are axially hinged to the balance beam through a pin shaft. The design structure of the equipment is simple. By the use of the variable-angle wheel set, the crane can adapt to a variety of construction-section pavements, thus improving production efficiency.