To investigate the run-up heights of nearshore tsunamis in the vicinity of a circular island, a numerical model has been developed based on quadtree grids. The governing equations of the model are the nonlinear shallow-water equations. The governing equations are discretized explicitly by using a finite difference leap-frog scheme on adaptive hierarchical quadtree grids. The quadtree grids are generated around a circular island where refined with rectangular or circular domain. Obtained numerical results have been verified by comparing to available laboratory measurements. A good agreement has been achieved.