In this work, we have investigated the domain wall (DW) depinning behavior in the notched nanowire by a micromagnetic simulation. A transverse domain wall (TW) was initially positioned at the center of notch and 1 ns length current pulse was applied to depin the DW with respect to the notch size s and the wire width variation. We have observed the depinning current density Jd which was a minimum current to escape DW from the notch. It was found that the depinning current density decreased as the wire width and the notch size increased. In the depinning process, we observed the inner structure of DW generally transformed from TW to anti-vortex wall (AVW). Interestingly, for the case of s less than 70 nm, AVW formed and depinned closely to the period when current pulse was active, while for s larger than 70 nm, AVW formed until the current pulse went to zero and then depinned after flipped TW was formed. It can be explained that the transformation of DW inner structures were affected by the spin torque energy and contributed to DW depinning behavior from the notched nanowires.