The system under consideration consists of a two-level atom coupled an optical field in k-photon Jaynes-Cummings model with a Kerr medium. The time evolution of field entropy squeezing and population inversion of the atom for three and four-photon transitions was discussed. The influence of Kerr medium on field entropy squeezing and population inversion of the atom was also analyzed. The results show that the field entropy squeezing and population inversion of the atom are sensitive to effect of Kerr medium.