Provided is an anti-vibration rubber composition, including the following components (A) to (D), in which a ratio of the component (B) to a total content of the components (A) and (B) is from 5 wt. % to 20 wt. %: (A) A natural rubber, or a blended rubber of the natural rubber and a butadiene rubber; (B) A hydrogenated styrene-butadiene block copolymer; (C) A sulfur-based vulcanizing agent; (D) Zinc monomethacrylate. Thus, there can be provided an anti-vibration rubber composition and an anti-vibration rubber each of which is excellent in heat resistance, and has both a high damping property and a low dynamic-to-static modulus ratio.