A novel composite resistive grating is presented. It is formed by combining two complementary resistive patterns. The problem of plane wave scattering by a two-dimensional resistive grating is considered. The formulation involves the concept of Fourier series expansion, which is manipulated to deal with the resistive boundary condition. The advantage of the formulation comparing with method of moments is that it can solve grating having arbitrary admittance distribution without doing reformulation process. Both conventional and composite resistive gratings are numerically investigated and characterized. Additionally, the equivalent circuit models of one-dimensional resistive gratings are acquired for TE and TM polarizations. Finally, the design of multilayered Jaumann absorbers incorporating conventional or composite resistive gratings are taken as numerical examples, where the accuracy of equivalent circuit models are verified. The proposed composite grating can increase the originally unavoidable small gap width from 0.1 mm to 0.4 mm in the Jaumann absorber design, which is proved to possess more design flexibility and higher tolerance to fabrication error than conventional one.