MgO polycrystal is found to be weakly magnetic experimentally, although its single crystal is non magnetic. In this work, the magnetic properties of surfaces of crystal and nano-particles of MgO are studied by the first-principles density functional theory. The obtained results show that there are the oxygen-rich regions in all the magnetic surfaces discussed in this work, especially in the (111) surface with pure oxygen layer and the (114) surface with pure oxygen chains. Other surfaces with high Miller indices generally have the oxygen-rich regions. For MgO nano-particles, the facets with high Miller indices and the edges and vertexes formed by different orientation surfaces are oxygen-rich possibly and have strong magnetism. The itinerant magnetism is indentified for the magnetism on the surfaces of MgO crystal and the surfaces of MgO nano-particles. That the special MgO ∑ 7[111] grain boundary is not magnetic means that the magnetism of MgO grain boundary is weak if the chemical composition in grain-boundary region is slightly different from that in the crystal. It can be inferred that the magnetism of MgO polycrystal is mainly contributed by the polycrystal surface, the micro-pores, micro-voids and micro-cracks.