Provided are a rubber composition which can give a crosslinked product with enhanced tensile strength, and a pneumatic tire including the rubber composition as a portion thereof. The rubber composition includes a solid rubber (A), a hydrogenated aromatic vinyl-conjugated diene random copolymer (B), and a filler (C). The random copolymer (B) satisfies the following (i) to (iv). (i) The content of aromatic vinyl units is 10 to 70 mass %. (ii) The vinyl content in conjugated diene units of the random copolymer (B) before hydrogenation is 10 to 70 mol %. (iii) The hydrogenation ratio of the conjugated diene units is not less than 10 mol %. (iv) The weight average molecular weight is 3,000 to 100,000.