Previous studies of shot noise suppression in nano-MOSFET either ignored its suppression or emphasized only its existence but gave no deeper research. In this paper, based on the Navid model, the expressions of shot noise suppression factor (Fano) in quasi-ballistic transport nano-MOSFETs are derived with separately considering Fermi effect, Coulomb interaction and the combination of the two effects. The variations of suppression-factors with source-drain voltage, gate voltage, temperature and source-drain doping are investigated. The results we obtained with considering the combination of the two effects are consistent with those from experiments, and the theoretical explanation is given.