Using self-consistent calculations of million-atom Schrodinger-Poisson equations, we investigate the I-V characteristics of tunnelling and ballistic transport of nanometer metal oxide semiconductor field effect transistors (MOSFET) based on a full 3-D quantum mechanical simulation under nonequilibtium condition. Atomistic empirical pseudopotentials are used to describe the device Hamiltonian and the underlying bulk band structure. We find that the ballistic transport dominates the I-V characteristics, whereas the effects of tunnelling cannot be neglected with the maximal value up to 0.8mA/mu m when the channel length of MOSFET scales down to 25 nm. The effects of tunnelling transport lower the threshold voltage V-t. The ballistic current based on fully 3-D quantum mechanical simulation is relatively large and has small on-off ratio compared with results derived from the calculation methods of Luo et al.