The propagation properties of Terahertz (THz) electromagnetic waves in a weakly ionized dusty plasma are introduced in this study. Epstein profile is adopted to describe the non-uniformity of the electron density in this simulation. By utilizing SMM approximation method, numerical calculation results show that dusty particles in plasma significantly affects the propagation. Specifically, the dusty plasma parameters have great influence on the reflection and transmission characteristics. Meanwhile, various interesting features concerning the reflection and transmission coefficients are obtained which are extremely important for the plasma sheath around the hypersonic vehicle.