The entropy properties of field in the system of coupled identical V-type three-level atoms interacting with vacuum field in cavity filled with Kerr-like medium are studied by means of quantum theory. The time evolution of entropy of field via the initial state of the atomic system, coupling coefficient between the atoms and Kerr coefficient are discussed. Numerical calculation results show that when the ground state and excited state of atoms are in appropriate superpositions state, the entropy of field is behaving periodic oscillation. The oscillation frequency and amplitude are depending on the coupling constant between atoms and the third-order nonlinear coefficient of Kerr-like medium. Therefore, the entropy of field is very sensitive to the atomic initial state.