To investigate the run-up heights of nearshore tsunami on the lee side of a circular island, a model has been developed on quadtree grids. The model is based on the Liu et al. using the shallow water equations. The result has been validated experimentally and numerically. The good agreement has been achieved. It should be noted that the run-up heights are mostly dependent on the crest length of incident waves when the crest length is less than the base diameter of the island but are almost insensitive if the crest length is greater than twice the base diameter.