Abstract In this paper we propose a robust adaptation method for hybrid mesh including both refinement and coarsening. Elements of different types are refined through isotropic subdivision in a similar way. Their unrefined neighbours are converted to polyhedrons, which benefits to localize mesh refinement. Mesh elements are coarsened by reversing refinement based on a multi-levels data structure. Elements subdivision can be conducted in entirely parallel mode by introducing a non-overlap number range for each processor. Then feature data is devised to recover the uniqueness of new ghost points and elements through parallel communication. A repartition-migration method is adopted to rebalance the computing load. We illustrate our method by an application of flow simulation. With mesh adaptation, the structures of shocks and vortices are resolved better.