The properties of the atomic inversion and the atomic state evolution are investigated by using the distance between density operaters in the intensity dependent coupling Janyes-Cummings model with an additional Kerr medium. The effect of nonlinearity interaction of Kerr medium and the average photon number of initial coherent field on the quantum properties of the atom are discussed. The result shows: the period of the atomic inversionis decreasing with the increase of the Kerr effect When the initialcoherent field is not great (n=10), the periodicity of the atomic state evolution is destroyed by Kerr effect, otherwise, when the initial coherent field is great (n=50), the atomic state evolution has periodicity approximately, also, the period is the same as atomic inversion Whether the average photon number of the initial coherent field is greator small, the probability that the atom locates initial state is increasing with the increase ofthe Kerr effect, when x/g=5, the atom always locates initial excited state nearly.