Using the numerical method, the information entropy and evolution of entanglement of atom and a single mode light field of Jaynes-Cumming (J-C) model in the Kerr effect medium cavity were studied. The influence of Kerr effect on the properties of entangled states was obtained. The results show that Kerr medium has a strong influence on entanglement property of coupled system. With the appropriate Kerr effect, the maximally entangled quantum state will remain long.