The present invention provides an acrylic rubber composition and its vulcanized product, having good vulcanization characteristics and an excellent balance between processability, mechanical properties of rubber and compression set.The acrylic rubber composition comprises a carboxyl group-containing acrylic rubber, a diazabicycloalkene compound, a polyamine compound, and a tertiary amine compound represented by the following formula (1): where each of R1, R2 and R3 is independently a substituent having at least one saturated aliphatic hydrocarbon or unsaturated aliphatic hydrocarbon having a linear structure, a branched structure or a cyclic structure, or benzyl group.