In this paper, the physical enhancement mechanisms of the surface-enhanced Raman scattering (SERS) of pyramidal tip substrates are studied theoretically. We structure the periodic square-based arrays of adjacent nanometer pyramidal gold-coated tips on silicon. In order to determine the contribution of plasmonic or diffraction effects on the SERS, three-dimensional (3D) numerical simulations are implemented by taking into account the substrate coated with a gold thin film or a perfect electrical conductor thin film. The tip distance, metal coating thickness and incident light polarization angle are also optimized to investigate whether the further SERS signal can be enhanced.