In this paper, a novel Wavelet-Galerkin Method (WGM) is presented to model the radio-wave propagation in tropospheric ducts. Galerkin method, with Daubechies scaling functions, is used to discretize the height operator. Later, a marching algorithm is developed using Crank-Nicolson (CN) method. A new"fictitious domain method"is also developed for parabolic wave equation to incorporate the impedance boundary conditions in WGM. In the end, results are compared with those from Advance Refractive Effects Prediction System (AREPS). Results show that the wavelet based methods are indeed feasible to model the radio wave propagation in troposphere as accurately as AREPS and proposed method can be a good alternative to other conventional methods.