In the present study, a new methodology in computational electromagnetics is developed for two-dimensional arbitrarily-shaped objects with impedance boundary conditions. The proposed approach investigates the E-polarized electromagnetic diffraction by a two-dimensional object with the Leontovich boundary condition. The scattered electric and magnetic fields are expressed as the convolution integral of the corresponding Green's function and the current induced on the obstacle surface. After obtaining integral equations by applying the boundary condition, the integral equations are solved as in the case of the method of auxiliary sources (MAS) which is a well-known method in computational electrodynamics. The results are compared with first, different methods such as the method of moments (MoM), orthogonal polynomials (OP), and second, different boundary conditions such as Dirichlet, Neumann, and fractional boundary conditions. Some results are also obtained for the different shape scatterers at some values of the surface impedance.