Polyhedral gold nanocrystals (Au NCs) with quasi-spherical, octahedral and triangle-like morphologies were synthesized using a hydrothermal method, and ordered packing structures were formed by water droplet evaporation-induced deposition. The self-assembled structures of the polyhedral Au NCs exhibit shape-directive arrangement during the building block orientation process, and the structure-dependent plasmonic characteristics of the self-assembled NCs were analysed numerically using the finite element method (FEM). The surface-enhanced Raman scattering (SERS) spectra of the self-assembled structures were measured by choosing 4-mercaptobenzoic acid as the Raman reporter, using an excitation wavelength of 785 nm. Both the theoretical and experimental results show that the self-assembled structures of polyhedral Au NCs have high electric field enhancements and excellent SERS performances, in particular, the octahedron self-assembled structures generate higher plasmonic enhancemence efficiency compared to other close-packed configurations. The superior SERS behaviours can be explained based on the electromagnetic enhancement mechanism and the plasmonic antenna effect of the interstitial hot spots, confirming that the self-assembly structures of polyhedral Au NCs offer an alternate way in the design of plasmonic enhancement substrates, with potential applications in bio-sensing and medical detection.