The statistic properties of photon in the system of two-mode entangled coherent field interacting with two identical two-level atoms in the Bell state in Kerr medium are investigated by means of quantum theory and numerical method. Induced by the atomic initial state, mean photon numbers of field, the degree of the entanglement for the entangled coherent fields, and the coupling strength of the Kerr medium with the light field, the effects on the statistic properties of photon are discussed. The results indicate that, if the medium is not present, photon anti-bunching effect does not appear for the Bell state β00〉 or β10〉, there can appear the photon anti-bunching effect under some conditions for the Bell state β01〉 or β11〉. If the medium is considered, there can appear the photon anti-bunching effect for all of initial states. In the case, the number of occurring , interval and intensity of the photon anti-bunching effects sensitively depend on the coupling strength of the Kerr medium with the light field, the mean photon numbers and the degree of entanglement of the two-mode entangled coherent field.