Surface integral equation methods have shown to be e?ective in solving large and multi-scale electromagnetic radiation and scattering problems. This is primarily due to the fact that both the analysis and unknowns reside only on the boundary surfaces of the targets. They are usually solved via the Galerkin method, which is based on a variational formulation in suitable trial and testing function spaces. Therefore, conforming boundary element spaces defined on a conformal discretization of the target's surface are commonly required. Subsequently, mixing di?erent types of basis functions, employing non-conformal discretizations, and/or incorporating the underlying physics to construct special basis functions within local regions are quite complicated. The goal of this research is to develop a discontinuous Galerkin method for surface integral equations, which employs discontinuous trial and testing functions without continuity requirements across element boundaries. The proposed work has advantages over the classical approaches in that different basis functions can be seamlessly integrated to best approximate the unknown currents locally. Another significant advantage of the method is that it can be applied conveniently to non-conformal discretizations and di?erent types of elements. In this way, the mesh generation task of complex, multi-scale targets can be facilitated considerably. The use of proposed method is justified through a practical example of an electromagnetic wave scattering from an electrically large multi-scale aircraft.