A vibration damping rubber composition is prepared containing the following components (B) to (E) together with a rubber compound prepared from the following (A). As a result, both heat resistance and the reduction of dynamic magnification factors can be achieved very satisfactorily. (A) A diene-based rubber containing natural rubber as a main component. (B) A filler. (C) A hydrazide compound. (D) A disulfide compound which is produced by the general formula (1) is shown. (E) A sulfur-based vulcanizing agent. [In the general formula (1), each of ring A and ring B denotes a nitrogen-containing heterocyclic group having 4 to 24 carbon atoms.]
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