Magnetic domain wall motion is numerically studied in a nanowire with a Dzyaloshinskii-Moriya interaction (DMI) step at which DMI varies in real space. The spatially modulated DMI results in the formation of asymmetric domain wall energy landscape across the step, which affects the domain wall motion significantly. Utilizing this DMI step, we propose a domain wall memory device where the switching of up-and down-state is induced by a spin-orbit spin-transfer torque (SOT)-driven domain wall motion. This domain wall memory device is expected to have a high switching efficiency. (C) 2017 Elsevier B.V. All rights reserved.