The annealing effect on the efficiency of current-driven domain wall motion governed by the spin Hall effect in perpendicularly magnetized Pt/[Co/Ni] wires is investigated experimentally. Important physical parameters, such as the Dzyaloshinskii-Moriya Interaction (DMI), spin Hall angle, and perpendicular anisotropy field strength, for the domain wall motion are all characterized at each annealing temperature. It is found that annealing of wires at temperatures over 120 ºC causes significant reduction of the domain wall velocity. Energy dispersive X-ray spectroscopy analysis shows pronounced Co diffusion across the Pt/Co interface resulted from annealing at relatively high temperatures. The combined modeling study shows that the reduction of DMI caused by annealing is mostly responsible for the domain wall velocity reduction due to annealing.