The statistical properties of the system consisting of a trapped ion and a single_mode quantized radiation field are investigated under the conditions of carrier excitation (ωL=ω0), red excitation ［ωL=ω０-jν(j=1,2,3)］ and blue excitation ［ωL=ω０+jν(j=1,2,3)］.The time_evolution of the state of the system,the photon_and phonon_state exchange conditions and the corresponding populations of the ion are discussed.The corresponding averages and variances for photon and phonon numbers,as well as the second_order correlation function for the photon and phonon fields etc,have been obtained.