The field entropy squeezing properties in the nonlinear Jaynes-Cummings model are studied by means of quantum information entropy, and the influences of the nonlinear interaction of the Kerr medium with the model field and the initial state of atoms on the field entropy squeezing are discussed. It shows that the nonlinear interaction of the Kerr medium can lead to an increase in the squeezing depth. On the other the squeezing time and the squeezing depth increases with the increase of the atomic distribution angle.