This paper presents a general variable neighborhood search (GVNS) heuristic for solving the maximum diverse grouping problem. Extensive computational experiments performed on a series of large random graphs as well as on several instances of the maximum diversity problem taken from the literature show that the results obtained by GVNS consistently outperform the best heuristics from the literature. [Projekat Ministarstva nauke Republike Srbije, br. ON174010 i br. III44006]