A high resolution finite volume method for solving the shallow water equations with voronoi mesh is developed applying MATLAB software in this paper. The scheme is formally uniformly second order accurate and satisfies maximum principles. The model is verified by comparing the model output with condition of anti-symmetric and circular dam break with documented results. For more investigation we utilized SPSS statistical software. Very good agreement has been achieved in the verification phase. It can be considered as an efficient implement for the computation of shallow water problems, especially concerning those having discontinuities. A simple example of the collapse of water supply reservoir in a valley is used to demonstrate the capability of the model. The presented model is able to resolving shocks, handling, complex geometry, including the influence of steep bed slopes.