Catalyzes the dehydrogenation of Glutaryl-CoA to glutaconyl-CoA. A + glutaryl-CoA = (2E)-glutaconyl-CoA + AH2 Inhibited by glutaconyl-CoA. Aromatic compound metabolism; benzoyl-CoA degradation. Homotetramer. Belongs to the acyl-CoA dehydrogenase family.