To provide a rubber composition suitable for a tread rubber of a high-performance pneumatic tire having good abrasion resistance and crashworthiness and providing excellent steering stability on a dry road.

The rubber composition is obtained by compounding (B) 1-200 pts.mass modified hydrogenated polymer comprising an aromatic vinyl-conjugated diene copolymer containing one or more kinds of polar groups selected from the group consisting of a carboxylic acid group, a sulfonic acid group, a carboxylate functional group and a sulfonate functional group in the molecule, and having 1.0103 to 2.0105 polystyrene-equivalent number average molecular weight and 20-100% hydrogenation rate of the conjugated diene part, and/or a conjugated diene polymer, and (C) 0.1-10 pts.mass compound containing zinc, with (A) 100 pts.mass matrix rubber comprising an aromatic vinyl-conjugated diene copolymer having 3.0105-3.0106 polystyrene-equivalent weight average molecular weight obtained by a gel permeation chromatography and polymerized by using a lithium-based polymerization initiator, and/or a conjugated diene polymer.