The Jaynes-Cummings models with a time-dependent atom-field coupling under the initial squeezed state of the optical field are discussed. Especially, the evolution of the atomic population inversion, and the squeezing properties of the field with time are studied. Further, the effects of the atom-field coupling coefficient, the squeezing parameter and phase on these properties are also discussed, and some results are obtained. With the increasing of squeezing coefficient, the frequency of collapse-revival in atomic population inversion are enhanced, and the amplitude of revival decreases, in the same time, there are no squeezing. When atom-field coupling coefficient changes rapidly, it will fasten the collapse-revival. With the increasing of squeezing phase, it will delay the collapse-revival and decrease the amplitude of revivals.