Coarse-grained, mesoscale simulations are invaluable for studying soft condensed matter because of their ability to model systems in which a background solvent plays a significant role but is not the primary interest. Such methods generally model passive solvents; however, far-from-equilibrium systems may also be composed of complex solutes suspended in an active fluid. Yet, few coarsegrained simulation methods exist to model an active medium. We introduce an algorithm to simulate active nematics, which builds on multi-particle collision dynamics (MPCD) for passive fluctuating nematohydrodynamics by introducing dipolar activity in the local collision operator. Active-nematic MPCD (AN-MPCD) simulations exhibit the key characteristics of active nematic turbulence but, as a particle-based algorithm, also reproduce crucial attributes of active particle models. Thus, mesoscopic AN-MPCD is an approach that bridges microscopic and continuum descriptions, allowing novel simulations of composite active-passive systems.