A two-dimensional mathematical model for simulating flow and sediment transport is presented. The model simulates flow and geo-morphological processes using a high order accurate, oscillation free scheme. The depth averaged Reynolds (shallow water) equations are used for flow simulation. Both equilibrium and non-equilibrium methods (by solving convection-diffusion equation) are used for sediment transport modeling while sediment carrying capacity is computed using different methods. A finite volume, flux difference splitting scheme is employed to solve the governing equations, which is able to simulate sub, super and transcritical flows with shock waves. Moreover, the numerical method is able to simulate flow over the variable topographies and it has a low level of numerical diffusion in the case of circulating flows like headlands. The computational grid of this model is triangular unstructured with variable size, which is flexible for arbitrary geometries and grid refinement. Using the model for simulating flow and sediment transport in some test cases such as a partially closed channel and comparing the results showed that the results obtained by the developed model were in a reasonable agreement with measurements and the other models cited.