The influence of nonlinear Kerr medium on non-classical correlations and quantum state transfer in an atom-cavity-fiber system with a cavity filled with nonlinear Kerr medium are investigated. Results show that Kerr medium can increase the amount of non-classical correlations and the fidelity of quantum state transfer, and slow down the decay rate of non-classical correlations and fidelity, which means that the time of non-classical correlation and quantum state transfer can be prolonged by adjusting Kerr medium. Furthermore, how Kerr medium affects the transfer of quantum information in the system is also explored by making use of the trace distance. It is found that the decay rate of trance distance can be reduced by Kerr medium, and the flow of quantum information can be suppressed as well, which indicates that the storage time of quantum information between target atoms can be increased.