Non-local transport characteristics of the deep sub-micrometer NMOS device are studied under electro-static discharge (ESD) stress. The result obtained shows that velocity overshoot may increase the drain current and has a great impact on the device characteristics, and that the energy relaxation time is correlated closely with the electric field of some point in the device as well as the velocity and the energy of the carriers, thus constant value is not appropriate for this parameter. The energy relaxation time and the high field mobility as functions of the carrier energy are gained by Monte Carlo calculation, and then device simulation is performed with these parameter models. Comparing ESD simulation with experimental results shows that accurate result about the I-V characteristics can be gained by using the models of the energy relaxation time and the high field mobility.