PURPOSE: To provide a lightweight tire reduced in the air permeability of its insulation ply and also reduced in the rubber thickness of its inner liner.

CONSTITUTION: The objective rubber composition comprising (A) 100 pts.wt. of a rubber component and (B) 2-4.5 pts.wt. of sulfur. The component A is composed of (1) 10-60wt.% of a natural rubber grafted with at least 1 pt.wt. of organic fibers, (2) 20-70wt.% of an epoxidized natural rubber 3-50mol% in degree of epoxidization and (3) the rest of a diene rubber. This rubber composition is useful for providing the insulation ply of pneumatic radial tires.