A novel hybrid algorithm combining the 3‐D vector finite element method‐boundary integral method (FEM‐BIM) with the half‐space Green’s function with the rough‐surface interface is developed in this paper to study the scattering from a 3‐D coated target above a perfectly electric conducting (PEC) rough surface. The half‐space Green’s function is derived from the Kirchhoff approximation (KA). The 3‐D vector FEM is applied to model the coated object, and the BIM with the half‐space Green’s function is selected as the exact radiation boundary conditions. The accuracy of our numerical code is validated by the numerical method. Some numerical results are provided to study the electromagnetic scattering characteristics from a coated sphere above a Gaussian rough surface.