In [1] we suggested an original Discrete Element Method that offers the capability to consider non spherical particles of arbitrary convex shape. We elaborated on the foundations of our numerical method and validated it on assorted test cases. However, the implementation was serial and impeded to examine large systems. Here we extend our method to parallel computing using a classical domain decomposition approach and inter-domain MPI communication. The code is implemented in C++ for multi-CPU architecture. Although object-oriented C++ offers high-level programming concepts that enhance the versatility required to treat multi-shape and multi-size granular systems, particular care has to be devoted to memory management on multi-core architecture to achieve reasonable computing efficiency. The parallel performance of our code Grains3D is assessed on various granular flow configurations comprising both spherical and angular particles. We show that our parallel granular solver is able to compute systems with up to a few hundreds of millions of particles. This opens up new perspectives in the study of granular material dynamics. (C) 2017 Elsevier B.V. All rights reserved.