In this paper, a physical model of graphene adsorption system is established. The interaction energy between graphene atoms and adatoms is calculated in the case of considering the anharmonic vibration of the atom and the electron-phonon interaction. By means of the statistical physics theory and method, we obtain the probability of adsorption adatoms and the temperature-dependence analytic equation of the number of mental atoms charge filling. Taking alkali metals as an example, we discuss the effect of the electron-phonon interaction and the atomic anharmonic vibration on the number of charge filling. The results show that the charge filling numbers of graphene adsorption system decrease linearly with the enlargement of distances of adatoms and increase nonlinearly with the increase of temperature and electron-phonon interaction energy. If the anharmonic vibration is neglected, the number of charge filling is independent of distance and temperature etc. The anharmonic vibration is more obvious when the temperature becomes higher or the electron-phonon interaction energy becomes smaller.
