In the system of many atoms interacting with many cavity fields respectively via intensity dependent coupling, the influence of Kerr medium on process of entangled information periodic transfer between the atoms and the cavity fields is studied by means of the complete quantum theory. It is found that Kerr medium does not influence on special cases which the initial cavity fields are vacuum states or entangled states superposing of the lowest Fock states, but the phase and period of entanglement information transfer are changed obviously for the general Fock states Ink) (nk 并0) in the presence of Kerr effect. The stronger the Kerr effect, the shorter the transfer period. The speed of the entangled information transfer can be controlled by choosing different Kerr medium. In the other hand, the alteration of the transfer phase has also close relation with the photon number nk (k = 1, 2, 3, . . . ,M) in the cavity fields.