The relations of erosion and sediment yield with their impact factors on the Loess Plateau of China have been a research focus.A relation model based on BP neural network model is constructed by taking 23 small watersheds on the Northern Shaanxi Loess Plateau as test areas.In the relation model,six impact factors are selected as input variables and erosion and sediment yield modulus,as output variable.The weighted matrix is employed to express the interface for input variables and hidden layers and the interface for hidden layers and output variable.Results show that the model can effectively distinguish the correlativity between the six impact factors and erosion—sediment yield modulus.From strong to weak,the six impact factors can be ordered as: soil anti-erodibilitynibble degreegully densityaverage annual precipitationNDVIthe ratio of silt to clay.Finally,the validity of the relation mode is verified by randomly selecting 3 small watersheds and employing BP neural network model.This study may be helpful to improve the methodology of the analyses of erosion and sediment yield in a watershed.