This thesis issues the quantum mechanical simulation of nano-scale MOSFETs in the ballistic transport regime. The main focus of this thesis is the device characteristics of a DG(Double-Gate) SOI(Silicon on Insulator) MOSFET, which is widely considered as the ideal device structure as the device size shrinks down to nanometer scale. This work discusses 1) properties of ballistic transport of carriers in nano-MOSFETs, and 2) the comparison of the DG(Double-Gate) MOSFET and the SG(single-gate) MOSFET in the ballistic case. The simulation was performed by using NEGF(non-equilibrium Green's function) formalism in the case where the effective channel length of device is comparable to the mean free path of electrons in the silicon channel. We investigated the I-V characteristics of the nano-MOSFETs in detail, and compared the device performance such as off-current, sub-threshold swing and threshold voltage between of the DG-MOSFET and the SG-MOSFET. We have found that the channel length may be reduced to 10~20 nm without much loss in the performance.