We present a structural analysis of the packings of identical non-spherical particles based on Voronoi cells. The packings are generated by discrete element method (DEM) simulations. The particles include axisymmetric ellipsoidal particles from oblates to prolates and cylindrical particles from disks to rods. The Voronoi cells are constructed by virtue of space discretization and surface reconstruction, which is shown to be universal for different shapes. The effects of particle aspect ratio and sliding friction coefficient on the properties of Voronoi cells, including the reduced volume, reduced surface area and sphericity, are quantified. The reduced volume and surface area are found to observe log-normal distributions, while their mean values and standard deviations have different dependencies on particle shape and friction. By analyzing the correlations and using inherent relationships between different Voronoi cell properties, we establish a group of universal equations to predict these distributions according to particle sphericity and overall packing fraction. Such findings can not only improve our understanding on the packings of non-spherical particles but also provide a basis for evaluating the transport properties and advancing the statistical mechanics theory for granular matter composed of non-spherical particles. (C) 2016 Elsevier Ltd. All rights reserved.