The time evolution of the linear entropies for the atom-field coupling system, the atom and the field in Tavis-Cummings model in the presence of phase damping of field is investigated. The effects of the initial field states, different value of decay constant and the initial atomic states on all the entropies are discussed.The results show that the different properties of the initial field prepared in the cavity can change the characters of all the linear entropies significatly.The evolution of the linear entropy of the system is independent of initial atomic preparation,but the linear entropy of the atom depends on the initial atomic state and independent of the cavity phase damping.