Temporal evolution is studied for total entropy, the entropy difference and the sum of negative eigenvalues of the partially transposed density matrix as quantitative entanglement measurements for JC model in a phase-damped cavity in the dispersive approximation. The cavity field is assumed to be coupled to a reservoir with a phase-damping coupling. The case of a statistical mixture (SM) of coherent states is considered as initial field state. The effects of cavity phase damping on the entanglement between the field and the atom are studied.