Abstract: The concept of time-dependent global attractors was recently presented by Di Plinio, Temam et al.~By using the skill of the operator decomposition, the asymptotic compactness of a family process \{U(t,\tau)\} corresponding to the plate equations with the coefficient dependent on time was proved,~and then the existence of time-dependent global attractors as well as the regularity were obtained under the condition that f satisfies the critical exponent growth