The invention discloses a method adopting vertical stay ropes to construct steel-concrete composite girders. Firstly, steel girder units are prefabricated, multiple temporary suspending pieces are arranged on flanges of steel girders in a spaced way, and meanwhile multiple groups of stay rope devices are correspondingly designed on a bridge girder erection machine; during construction, first holedsteel girder units are erected in place, then suspension clasps at the bottoms of the stay ropes on the bridge girder erection machine are connected with the suspending pieces on the flanges of steelgirders to make the stay ropes in a vertical state, then rope forces of the stay ropes reach set value through stretching and drawing, and then the stay ropes are locked; prefabricated concrete bridge deck slabs are installed; bridge deck slab wet joint concrete is poured, and after the bridge deck slab wet joint concrete reaches the design strength, connection between the stay ropes and the suspending pieces is relieved; then, second holed steel girder units are erected to complete 'simple-bracing variable-continuity' system conversion of two-holed steel girders is completed; by this analogy, construction of a whole connected bridge is completed. The method can improve the material utilization efficiency of traditional support-free steel-concrete composite girder construction, has a series of advantages of quick and convenient construction and the like and has the wide application prospect in large-medium-span composite girder erection.