Abstract: The cusp-catastrophe theory of nonlinear science is applied for studying transport rate of bed load in this paper.By means of analyzing the factors effecting incipient motion of sediment, the state variable and the bound variable in cusp-catastrophe model are obtained, and the cusp-catastrophe model being able to reflect the transport of bed load is built Based on the standard equation of the cusp-catastrophe, the function between the bed load intensity Φ and Shields number Θ is derived by using coordinate transform and topology transform.The bed load intensity Φ is regarded as the state variable, and Shields number and coefficient of condensing of bed material m are regarded as bound variable in cusp-catastrophe model.Flume experiment data and other formulas are used to verify the cusp-catastrophe model, it indicates that the results calculated from the cusp-catastrophe formula agree well with the flume experiment data and the results calculated by other formulas.This indicates that the cusp-catastrophe formula derived here is reasonable, and the results can reflect the characterist ics of transport of non-uniform sediment.The purpose of this paper is to explore the incipient motion and transport laws of non-uniform sediment from the viewpoint of nonlinear theoty.