Abstract: Based on the algorithm frame of finite volume on unstructured grids,by introducing upwind decomposition of flow and sediment numerical fluxes in the normal direction to and across each side of cells,a 2-D finite volume method for flow and sediment movements is established,including exchange modes between suspend sand and bed sand,and sediment-carrying capacity formula of different grain.The algorithm is used to simulate the numerical value on flow and sediment transport and riverbed deformation.It is proved that this algorithm can reflect the dynamic process of flow and sediment transport and river bed deformation,and that the precisions satisfy the analytic need of the river engineering.