As an unstructured-grid high efficient solver, the multigrid algorithm, with its serial and parallel application, can achieve the optimal properties of being on time and having space complexity. To illustrate the numerical simulation process of an unstructured grid, this paper begins with the discretization of governing equations and points out that the multigrid algorithm is mainly used for solving large scale algebraic equation, which is derived from the time marching scheme. For the multigrid algorithm, the study briefly describes its basic structure and efficient principle. Secondly, the paper reviews research that trend about the geometric multigrid and algebraic multigrid and discusses the basic design principles and hot topics on parallelization. At the same time, for the practical application of unstructured grid, the paper summarizes and classifies many smoothers, followed by examples of open source software about unstructured grid industrial application. Finally, some applications and key problems in this field are highlighted, as well as the future progress of parallel multigrid solver on unstructured grid.