We investigate the current-induced domain wall motion in perpendicular magnetized Tb/Co wires with structure inversion asymmetry and different layered structures. We find that the critical current density to drive domain wall motion strongly depends on the layered structure. The lowest critical current density ∼15MA/cm2 and the highest slope of domain wall velocity curve are obtained for the wire having thin Co sublayers and more inner Tb/Co interfaces, while the largest critical current density ∼26MA/cm2 required to drive domain walls is observed in the Tb-Co alloy magnetic wire. It is found that the Co/Tb interface contributes negligibly to Dzyaloshinskii-Moriya interaction, while the effective spin-orbit torque strongly depends on the number of Tb/Co inner interfaces (n). An enhancement of the antidamping torques by extrinsic spin Hall effect due to Tb rare-earth impurity-induced skew scattering is suggested to explain the high efficiency of current-induced domain wall motion.