Based on the confluences of the different rank streams, a dynamical model of sediment transport in river network is proposed. A river can be divided into segments by the injection of branch streams of higher rank. Since there are no large fluctuations in stream flow and sediment concentration in a lower-water season, the real process in the river network can simulated by our model. With the model, the steady state indicates a scaling law that the quantity of erosion or sedimentation exponentially depends on the number of the segments along the reach of the channel. We also discuss the influence of the model's parameters on steady scouring-deposition under larger impact factors. The result reveals abundant scouring- deposition phenomena which are coincident with natural river networks.