The invention discloses a fixed hoisting bracket device for pushing a steel box girder and a construction method thereof. The fixing crane bracket device comprises fixed hoisting bracket main beams, a hoisting system, a hanging carrying pole beam, a hanging beam section, a beam-transporting ship, a front supporting leg, a front supporting leg base, a slide rail, a back supporting leg hinged support, a back supporting leg upright column, a poured beam section, a guide beam, an erected beam section, an assembly platform slide rail, an assembly platform, a hoisting system slide rail and a horizontal connecting structure between the fixed hoisting bracket main beams. The construction method thereof comprises the following steps of: assembling and erecting the fixed hoisting bracket, arranging the hoisting system of the fixed hoisting bracket, hoisting the steel box girder, transforming the system of the steel box girder and assembling the steel box girder. The fixed hoisting bracket device has the advantages that: the steel box girder is stably, rapidly, continuously and uniformly hoisted in place; a pushing platform of the steel box girder or a beam top of the erected beam section is used as a supporting point of the front supporting leg of the fixed hoisting bracket to decrease the support height of the supporting leg to a bed and save the processing amount of steel structure; the bracket structure can bear force simply and clearly; the materials are convenient to acquire and are rapidly assembled; and the fixed hoisting bracket device is easy to popularize.