In this paper, the evolution of field entropy of the interaction between A-type three-level atom and single-mode coherent field in a Kerr medium is studied. The influences of the Kerr medium and of the initial mean photon number n (the initial field intensity) on the entropy is discussed. It has been shown that the periodicity of the evolution curves of the field-entropy is influenced by the initial mean photon number n. With the increase of the initial field intensity n, the mean values of the evolution curves of the field entropy increase constantly when the initial field intensity n is not big (about n<40), therefore, the related degree of the field-atom strengthens. And in the condition of strong field (about n > 40), with the increase of the initial field intensity n, the related degree of the field-atom decreases constantly and disappears. The Kerr medium intensity parameter μ also has influences on the periodicity of the evolution curves of the field- entropy. With the increase of μ, the Rabi oscillation frequency of the evolution cruves of the field entropy becomes rapid obviously.But tis maximal value decreases constantly.This shows that the field entropy is susceptible to the non-linearity action of Kerr medium.And the non-linearity action of Kerr mediumcam weaken the interaction of the field-atom.