A multi-block overset grid method is presented to accurately simulate viscous flows around complex configurations. A combination of multi-block and overlapping grids is used to discretize the flow domain. A hierarchical grid system with layers of grids of varying resolution is developed to ensure inter-grid connectivity within a framework suitable for multi-grid and parallel computations. At each stage of the numerical computation, information is exchanged between neighboring blocks across either or both matched block boundaries and overlapping boundaries. Coarse-grain parallel processing is facilitated by the multi-block system. Numerical results of flows over multi-element airfoils and three-dimensional turbulent flows around wing–body aerodynamic configurations demonstrate the utility and efficiency of the method.