A rubber composition includes a diene rubber (A), a silica (B), a silane coupling agent (C), and an acid-modified polyolefin (D); the diene rubber (A) containing not less than 30 mass % of an aromatic vinyl-conjugated diene copolymer rubber; the acid-modified polyolefin (D) having at least one type of repeating unit selected from the group consisting of propylene, 1-butene, and 1-octene; a content of the silica (B) being from 5 to 150 parts by mass per 100 parts by mass of the diene rubber (A); and a total content of the silane coupling agent (C) and the acid-modified polyolefin being from 5 to 30 parts by mass per 100 parts by mass of the diene rubber (A). Such rubber composition is capable of achieving both excellent vulcanization properties and low heat build-up. A pneumatic tire includes such rubber composition.