The Maxwell′s equation of terahertz wave in time-varying plasma is deduced based on time-domain finite difference method of auxiliary differential equation in this paper. A time-varying plasma model with dust particles was constructed by using the constitutive relation. The absorption coefficient, reflection coefficient and transmission coefficient of the dust plasma sheath with time were simulated. The numerical results show that the growth rate of electron density is easily affected by the rise time, and the reflection coefficient of the plasma decreases with the increase of the rising time. The increase of the absorption coefficient is related to reducing the rise time and frequency, increasing the electron density and the density of the dust particles.In addition, the thickness of the plasma plate, the density of the dust particles, and the electron density are direct proportional to the absorption coefficient. When the operating frequency of the wave up to 1 500 GHz, only the electron density is less than 1020 m－3 can pass through the plasma plate. The alteration of the effective collision frequency barely affects the reflection coefficient of the time-varying dusty plasma as the collision frequency is smaller than 3.5×1011 rad/s. The results provide some technical support for the potential applications of spacecraft in the atmosphere of terahertz communication and dust plasma diagnostics.