Depinning fields of a magnetic domain wall (DW) from asymmetric notches artificially introduced into submicron magnetic wires were investigated by utilizing the giant magnetoresistance effect. It was found that the depinning field from the asymmetric notch depends on the propagation direction of the DW. The asymmetric notch works as an asymmetric potential barrier against the DW propagation. The depinning field increases with increasing slope of the asymmetric notch.