Using the method of the systematic state vector we formulate the entropy of the V-type three-level atom interacting with initially uncorrelated two-mode coheren t states of arbitrary detunings in a cavity filled with Kerr-like medium. It is shown by numerical calculation that the behavior of the entropy is strongly affe cted by the Kerr medium. Weak Kerr medium improves the quantum correlation. Stro nger Kerr medium induces strongly periodic fluctuation of the quantum correlatio n between the atom and the fields.