Previous investigations of non-equilibrium and equilibrium sediment transport are analyzed and a two dimensional (longitudinal profile) mathematical model of non-equilibrium sediment transport in river channels with non-uniform bed material is presented in this paper The concept of exchange rate of bed material is introduced, and a very short time step is used in the calculation. The distance for sediment recovering equilibrium for the non-uniform bed material is far longer than that for uniform bed material and the mechanism of the phenomenon is discussed. Because the size of bed material is coarsened, the scouring of sand is far less than that for the initial state and the distance of non-equilibrium sediment transport becomes much longer. A slower exchange rate of bed material then leads to a longer distance of non-equilibrium sediment transport. Previous investigations of non-equilibrium and equilibrium sediment transport are analyzed and a two dimensional (longitudinal profile) mathematical model of non-equilibrium sediment transport in river channels with non-uniform bed material is presented in this paper The concept of exchange rate of bed material is introduced, and a very short time step is used in the calculation. The distance for sediment recovering equilibrium for the non-uniform bed material is far longer than that for uniform bed material and the mechanism of the phenomenon is discussed. bed material is coarsened, the scouring of sand is far less than that for the initial state and the distance of non-equilibrium sediment transport becomes much longer. A slower exchange rate of bed material then leads to a longer distance of non-equilibrium sediment transport .