When forming a rubber member which is made up of a combination of a plurality of rubber compounds by winding spirally a ribbon-shaped unvulcanized rubber strip material in an overlapping fashion, the number of times of winding is reduced so as to shorten a fabrication cycle time of the rubber member to thereby increase the productivity thereof. As a means therefore, a rubber strip material whose cross section is divided into two or more regions which are made up of different rubber compounds is wound spirally on to a drum in an overlapping fashion so as to build a green tire or a tire rubber member.