Abstract: In this work, we study the rate of sediment transport on bed slopes based on the formula of Engelund to derive a theoretical formula of the transport rate with a wide application range. A formula of the probability of sediment incipient motion on bed slopes is also derived through analysis of the forces on a sediment particle on a bed slope and considering the stochastic flow velocity and stochastic position of the sediment particles on the bed. Then, we improve the formulas for calculating the number of sediment particles on a unit area of bed and the velocity of bedload sediment, and obtain a formula of the transport rate of bedload sediment on bed slopes. Results show that our formula feature a high accuracy of calculation and a good applicability to different bed slopes, which is verified by using the measured data of different bed slopes and comparing with the classical formulas.