The complete understanding of domain wall (DW) dynamics is important in the design of future spin-tronic devices. The characteristics of faster time-scale and lower current amplitude to move DW along nanowire are crucial in fabrication upgrade. In this study, we have investigated depinning behavior of magnetic domain wall triggered by nanosecond current pulse in notched Permalloy nanowires by means of micromagnetic simulation. We introduced double-triangular notch as the constrictions in the nanowire. The non-adiabaticity of the spin-transfer-torque is considered in simulation by varying the non-adiabatic constant (beta) value. We observed that the depinning current density (J(d)) was not significantly affected by beta for notch size (s) < 50 nm. Interestingly, we found that the depinning time (t(d)) for beta >= 0.04 was slightly constant for all the cases with s > 70 nm, where the DW structure was kept to be a transverse structure during the depinning process. The broadly applicable depinning behavior is considered to contribute to the development of high-speed memory storage devices based on magnetic domain wall. (c) 2017 Elsevier B.V. All rights reserved.