A conjugated diolefin copolymer rubber is produced by copolymerization of a conjugated diolefin and an aromatic vinyl compound and has a primary amino group and an alkoxysilyl group bonded to the copolymer chain. The conjugated diolefin copolymer rubber contains the aromatic vinyl compound in an amount of 5 to 60 wt %. The aromatic vinyl compound is densely distributed in one terminal of the copolymer chain, and is scarcely distributed in the other terminal. The conjugated diolefin copolymer rubber has a temperature difference (ΔTg) of 25° C. or more. The conjugated diolefin copolymer rubber has low hysteresis loss properties as well as improved abrasion resistance, rupture characteristics, and road grip characteristics without impairing wet skid characteristics. A method for producing the conjugated diolefin copolymer rubber is also disclosed.