A hybrid approach combining the edge-based vector finite-element method (FEM) and the method of moments (MoM) is first extended to study 3-D scattering from a dielectric object above a conductive rough surface. The hybrid FEM/MoM technique is based on the electric field vector Helmholtz's equation. To reduce the calculational domain, the solution region is divided into the FEM region containing the object and the MoM region containing the rough surface. In our hybrid method, tetrahedral elements are applied to handle the object region based on vector basis functions, whereas triangular elements are used to deal with the rough surface based on Rao-Wilton-Glisson basis functions. The electromagnetic coupling between the object and the rough surface is considered by the surface integral equation with the Green's function. The hybrid technique presented here combines advantages between FEM and MoM, which is highly efficient in terms of computing memory, time consumed, and versatility.