The dispersion relation and Landau damping of electron plasma waves in the quantum plasma are derived by kinetic theory. Starting from the quantum hydrodynamic equation of electron and photon kinetic equation, photon Landau damping is discussed. Research indicates that quantum effects enlarge the frequency of electron plasma waves and do not change the dispersion of electromagnetic waves. It is also found that electron and photon Landau damping rates are both reduced by quantum effects, so the exchange of energy between particles and waves is retarded.