We have proven that the Schrodinger cat states can be generated by conditional measurement on the atom in the Jaynes Cumming model with a Kerr like medium. The special states such as even coherent states, odd coherent state and Yurke Stoler coherent state may be aqcuired by further choosing some suitable parameters, such as the time of measurement, initial state of the atom, and Kerr nonlinear constant. The sub poisson distribution can be revealed under the high field approximation (n>>1) only in the existence of Kerr medium.