The inability of simulating the grain shapes of granular media accurately has been an outstanding issue preventing particle-based methods such as discrete element method from providing meaningful information for relevant scientific and engineering applications. In this study we propose a novel statistical method to generate virtual 3D particles with realistically complex yet controllable shapes and further pack them effectively for use in discrete-element modelling of granular materials. We combine the theory of random fields for spherical topology with a Fourier-shape-descriptor based method for the particle generation, and develop rigorous solutions to resolve the mathematical difficulties arising from the linking of the two. The generated particles are then packed within a prescribed container by a cell-filling algorithm based on Constrained Voronoi Tessellation. We employ two examples to demonstrate the excellent control and flexibility that the proposed method can offer in reproducing such key characteristics as shape descriptors (aspect ratio, roundness, sphericity, presence of facets, etc.), size distribution and solid fraction. The study provides a general and robust framework on effective characterization and packing of granular particles with complex shapes for discrete modelling of granular media. (C) 2014 Elsevier B.V. All rights reserved.