A numerical model applicable to shallow water flows in rivers and over flooding area with complex geometry is of great interest to hydraulic researchers and engineers. In this paper, an explicit conservative CIP scheme for shallow water flows is developed based on the control volume method. The scheme simultaneously solves point, line and area averaged values of a computational cell to directly capture the variations of flow and geometry within the cell. Comparisons between numerical results and exact solutions for a one-dimensional dam break problem confirmed the superiority of the present scheme over conventional schemes in terms of accuracy. And other two tests also demonstrated that the present scheme with coarse cells can yield the reliable results for complex flows over undulated bed configuration.