Degree of degeneracy of quantized inversion layer in metal-oxide semiconductor structure are investigated by a fully quantum mechanical approach via self-consistent solution of Schrodinger and Poisson equations. The relative error of carrier sheet density induced by Boltzmann statistics is used as a measurement of the degeneracy. It is shown that the degree of degeneracy of inversion layer is much weaker due to the quantization of carrier energy compared with the semi-classical one.