This paper presents a numerical study on the self-assembly of mono-size granular spheres with periodic boundary conditions under uniform and non-uniform 3D vibration. For uniform 3D vibration, the vibration conditions for self-assembly are similar to those under 1D vertical vibration. For non-uniform 3D vibration, slight horizontal vibration added to 1D vertical vibration can significantly promote or depress self-assembly. Moreover, under 1D or uniform 3D vibration, self-assembly results in a RHCP (random hexagonal close packed) structure, while under certain non-uniform vibration, a packing can self-assemble into a nearly pure FCC (face centered cubic) or HCP (hexagonal close packed) crystal structure. The microscopical analyses on the local structures, dynamics and forces provide rich insight into the different self-assembly processes under different vibration modes. These results can help understand the self-assembly of granular materials under vibration and guide how to control the structure of packed beds. (C) 2020 Elsevier B.V. All rights reserved.