Two-photon Jaynes-Cummimgs model is generalized to the case of Kerr medium in this paper. The field and atom are prepared initially in two-photon superposition state and ground state respectively. Nonlinear coefficient affects the dynamic behaviors of the field and atom. Evolutions of the squeezing for the operators of field and atom and the quantum inversion are discussed. In particular, the higher-order squeezing for atomic dipole and the effects of nonlinearity on it, which have not been studied by other authors,are investigated. Increasing the nonlinear coefficient will decrease the squeezing depth of atomic dipole.