The quantum statistical properties of two-photon Jaynes-Cummings model with a time-dependent atom-field coupling coefficient are discussed under the initial squeezing state of the light field. Especially, the time evolution of the atomic population inversion and the squeezing properties of the cavity field is investigated. The effects of the atom-field coupling coefficient, the squeezing parameter and phase on these properties are also discussed. When the squeezing coefficient of the initial field increases, the frequency of collapse-revival in atomic population inversion increases, and the amplitude of revival decreases. When the atom-field coupling coefficient changes slowly, the collapse-revival is delayed, and the squeezing of the field is lost gradually. When the coupling coefficient changes rapidly, it accelerates the collapse-revival phenomena, and the squeezing parameter oscillates with time, the squeezing of the field appears repeatedly.