In this paper, a theoretical method based on the discrete electronic states is proposed to calculate the Fermi-level of metal nanoparticles embedded in an insulator. According to the calculations, the structures of metal nanoparticle energy level are acquired. Meanwhile, the new formula for evaluating the size of metal nanoparticle by using the information about the surface plasmon resonance peak is also provided. Many known phenomena related to the metal nanoparticles can be explained by this theory. The calculation results on size of nanoparticle are found to be in good agreement with the AFM measurements for high dose Cu implanted Si3N4/Si samples.