We study the high-field-driven motion of a magnetic domain wall (DW) in a (Co/Ni) nanowire under the Dzyaloshinskii–Moriya interaction (DMI) by using micromagnetic simulations. The results show that the DW velocity above the Walker field (Hw) changes in response to not only the DMI strength but also the width of the nanowire. The DW velocity shows a re-increment depending on the magnetic field and reaches several hundred m/s, despite high-field regions above Hw. In the re-increment, the DW moves while maintaining its structure because the motion of vertical Bloch lines is blocked by the bending region of the DW.