The packing of uniform fine spherical particles ranging from 1 to 1000 μm has been simulated by means of discrete particle simulation. The packing structure is analyzed, facilitated by the well established Voronoi tessellation. The topological and metric properties of Voronoi polyhedra are quantified as a function of particle size and packing density. The results show that as particle size or packing density decreases, (i) the average face number of Voronoi polyhedra decreases, and the distributions of face number and edge number become broader and more asymmetric; (ii) the average perimeter and area of polyhedra increase, and the distributions of polyhedron surface area and volume become more flat and can be described by the log-normal distribution. The topological and metric properties depicted for the packing of fine particles differ either quantitatively or qualitatively from those reported in the literature although they all can be related to packing density. In particular, our results show that the average sphericity coefficient of Voronoi polyhedra varies with packing density, and although Aboav-Weaire's law is generally applicable, Lewis's law is not valid when packing density is low, which are contrary to the previous findings for other packing systems.