Using the perturbation method, a time dependent parabolic equation is developed based on the elliptic mild slope equation with dissipation term. With the time dependent parabolic equation employed as the governing equation, a numerical model for wave propagation including dissipation term in water of slowly varying topography is presented in curvilinear coordinates. In the model, the self-adaptive grid generation method is employed to generate a boundary-fitted and varying spacing mesh. The numerical tests show that the effects of dissipation term should be taken into account if the distance of wave propagation is large, and that the outgoing boundary conditions can be treated more effectively by introduction of the dissipation term into the numerical model. The numerical model is able to give good results of simulating wave propagation for waters of complicatedly boundaries and effectively predict physical processes of wave propagation. Moreover, the errors of the analytical solution deduced by [Kirby, J.T., . Parabolic approximation for water waves in conformal coordinate systems. Coastal Engineering 23, 185-213.] from the small-angle parabolic approximation of the mildslope equation for the case of waves between diverging breakwaters in a polar coordinate system are corrected.