In this article, we investigate the effects of phase damping on the temporal evolution of different entanglement measurements and the amount of entanglement for the damped Jaynes-Cummings model. The master equation is solved for any initial state in the two-level atom. Superpositions of two coherent states (π/2 or π out of phase) and their statistical mixture state are taken as initial states when a phase-damped cavity is taken into account.