A surface mesh represented discrete element method (SMR-DEM) for granular systems with arbitrarily shaped particles is presented. The particle surfaces are approximated using contact nodes obtained from surface mesh. A hybrid contact method which combines the benefits of the sphere-to-sphere and sphere-to-surface approaches is proposed for contact detection and force computation. The simple formulation and implementation render SMR-DEM suitable for three-dimensional simulations. Furthermore, GPU parallelization is employed to achieve higher efficiency. Several numerical examples are presented to show the performance of SMR-DEM. It is found that on the particle level the method is accurate and convergent, while on the system level SMR-DEM can effectively model particle assemblies of various regular and complex irregular shapes. (C) 2020 Elsevier B.V. All rights reserved.