The entropy evolution properties of the field in the system of a cascade three-level atom interacting with binomial field in a Kerr-like medium is studied. By numerical method, the results indicate when the atom initially in excited states, the field entropy increases with the increasing of Kerr coefficient, the quantum entanglement is improved too. However, the field entropy reduces when the parameter exceeds a certain value and the period of field entropy becomes longer. When the atom initially in levels’ superposition states, the field entropy reduces with the effect of Kerr effect and the entanglement between atom and optical field becomes lower. The field entropy could be improved unless the parameter exceeds a certain value. Then the law is the same as the case of the atom initially in excited states with the increasing of Kerr coefficient.