A diene polymer rubber composition comprising (A) 100 parts by weight of a raw material rubber comprising (A-1) a diene rubbery polymer which is a conjugated diene rubber polymer or conjugated diene-styrene rubbery copolymer (1) containing a modified component in an amount exceeding 60 wt. %, which modified component is obtained by reacting an active end of the rubbery polymer with a polyfunctional compound having, in its molecule, at least two epoxy groups, (2) having a molecular weight distribution Mw/Mn of 1.05 to 3.0, and (3) having weight-average molecular weight of 100,000 to 2,000,000; and based on 100 parts of the component (A), (B) 1-100 parts by weight of rubber extension oil, (C) 25-100 parts by weight of reinforcing silica, and (D) 1.0 to 20 parts by weight in total of a vulcanizing agent and a vulcanizing accelerator.