There is provided a pneumatic radial tire for a motorcycle, which reduces a difference between rigidities of the center section and the shoulder sections of a tread section to simultaneously provide a long wear life, high grip force, and high-speed durability without impairing linear characteristics of handling. It is a pneumatic radial tire for a motorcycle having a carcass 1 and a belt layer 2. A tread section is formed of a center section rubber 3, disposed in a widthwise center region of the tire and on both sides of a tire equator, and both side rubber 4, disposed on both widthwise ends of the tire. In addition, the tread section has a structure in which the center section rubber 3 and the both side rubber 4 are successively laminated upon each other at both widthwise ends of the tire. Further, the ratio of the thickness of both side rubber 4 in the tread section increases towards both widthwise ends of the tire, and a modulus of the both side rubber 4 is less than a modulus of the center section rubber 3.