In this paper, a robust and adaptive framework of finite volume solutions for steady Euler equations is introduced. On a given mesh, the numerical solutions evolve following the standard Godunov process and the algorithm consists of a Newton method for the linearization of the governing equations and a geometrical multigrid method for solving the derived linear system. To improve the simulations, an h-adaptive method is proposed for more efficient discretization by means of local refinement and coarsening of the mesh grids. Several numerical issues such as the regularization of the system, selection of the reconstruction patch, treatment of the curved boundary, as well as the design of the error indicator will be discussed in detail. The effectiveness of the proposed method is successfully examined on a variety of benchmark tests, and it is found that all simulations can be implemented well with one set of parameters, which shows the robustness of the method. © Springer International Publishing AG, part of Springer Nature 2018.