A vibration damping rubber composition having an excellent vibration damping performance includes the following (A) to (C) as essential components: (A) a diene-based rubber; (B) a vulcanizing agent of a bismaleimide compound represented by the following formula (1): [wherein X denotes a substituted or unsubstituted aliphatic saturated hydrocarbon group; and R1 to R4 may be the same or different and each denote a hydrogen atom, an alkyl group, —NH2, or —NO2, provided that the bismaleimide compound represented by formula (1) excludes a compound in which X is —(CH2)n- (n is an integer of 4 to 12) and all R1 to R4 are hydrogen atoms], wherein the vulcanizing agent is sulfur-free; and (C) a vulcanization accelerator.