Switching characteristics of dark soliton in asymmetric nonlinear directional couplers are numerically studied. Every individual effect, responsible for producing asymmetry in nonlinear directional coupler, has been analyzed in detail. It is found that group-velocity mismatch and the difference in group-velocity dispersions between the two cores have no impact on dark soliton, which can be specified as an advancement over the bright solitons. The effects of phase velocity, the difference in effective mode areas and the linear coupling coefficient on the dark soliton switching are also investigated.