A tire for a two-wheeled vehicle, particularly, a bicycle intended for a racing purposes having an improved running stability, superior durability and impact resistance, and reduced weight. The tire includes a carcass layer formed by arranging cord belts with a rubber paste coated thereon in such a manner that the cords of the cord belts cross each other. A tube is fitted to the inside of the carcass layer, and a rubber tread portion is bonded to the outer periphery of the carcass layer. The cord belt is produced in bias form with alternately arranged cords superior in durability and impact resistance and cords superior in adhesion with rubber. The two types of cords may be equal in number, or a majority of one of the two types of cords employed, depending upon the precise application of the tire and the conditions under which it is intended for use.