A pneumatic radial tire comprises a carcass comprising an outer carcass ply made of cords having a first heat-shrinkage-percentage K1 and an inner carcass ply is made of cords having a second heat-shrinkage-percentage K2 different from the first heat-shrinkage-percentage K1, and the cord tension of the inner carcass ply is smaller than the cord tension of the outer carcass ply. A method of making the tire comprises steps of making the outer carcass ply of cords having a first heat-shrinkage-percentage K1, making the inner carcass ply of cords having a second heat-shrinkage-percentage K2, wherein the first heat-shrinkage-percentage K1 at 150 degrees C. is 120 to 160% of the second heat-shrinkage-percentage K2 at 150 degrees C., and heating and vulcanizing a raw tire to heat-shrink the outer carcass ply cords in a larger degree than the inner carcass ply.