The entanglement dynamics of system,where atoms A and B interact with single mode cavity fields a and b respectively,is studied.The interaction between atom A and cavity a may be described by using the typical Jaynes Cummings model,while that between the atom B and cavity b filled with a Kerr medium is of a two-photon process.For a certain initial atom entanglement state,there is an entanglement sudden death effect between the two atoms.The Kerr medium in the cavity b can effectively prevent the undesirable entanglement sudden death from occurring.Also,from the viewpoint of the population dynamics,we discuss why the Kerr medium can do so.