We performed macro-spin simulation studies of the current-induced magnetization reversal of nanomagnetic elements with short current pulses. A special attention was paid to the effect of the energy barrier on the switching current distribution. The switching current and its distribution increase with decreasing the current pulse-width. The relationship between the energy barrier and switching current distribution is described by the Arrhenius-Néel law at a long pulse-width regime. At a regime of short pulse-width, however, the relationship is left unaddressed. The difficulty to address this issue arises because the magnetization switching with a short current pulse is governed not by the thermal activation but by the precession motion. Therefore, an exact formulation for the short pulse regime by solving the Fokker-Plank equation is needed to understand the result.