In this paper,the evolution of field entropy in the system of single-mode coherent light field interacting with a three-level cascade type atom is calculated exactly in the frame of complete quantum theory and without rotating wave approximation.The numerical results indicate that with the increases of the initial mean photon number n and the atom-field coupling strengths u and v the mean value of the field entropy increases at first and then decreases.Therefore,the degrees of entanglement also increase at first and then decrease.The mean value of the entropy of the field decreases with the enlarging of the detuning Δ, which leads to the decrease of the degrees of entanglement.