A pneumatic radial tire comprises a carcass comprising an outermost ply and an inner next ply, each made of organic fiber cords, a belt comprising a radially innermost ply and a radially outer next ply, each made of steel cords, a first damping rubber layer disposed between the outermost carcass ply and the inner next carcass ply, and a second damping rubber layer disposed between the outermost carcass ply and the radially innermost belt ply, the first damping rubber layer has an axial width of 0.8 to 1.2 times the axial width of the radially innermost belt ply and a thickness of 0.5 to 2.0 mm, and the second damping rubber layer has an axial width of 0.8 to 1.2 times the axial width of the radially innermost belt ply and a thickness (T2) of 0.5 to 2.0 mm, thereby the running noise is reduced without sacrificing running performance.