Neogene red clay is a typical weak layer associated with the occurrence of many landslides in the Chinese Loess Plateau. Understanding and modelling the creep behaviour of Neogene red clay is crucial for revealing, forecasting, and preventing landslides. However, there is still a lack of appropriate descriptions for the stress-dependent creep behaviour of Neogene red clay. To remedy this issue, a series of direct shear creep tests for saturated Neogene red clay are performed. Test results show that saturated Neogene red clay exhibits apparent creep deformation and that its creep behaviour is closely associated with shear stress and normal stress. Based on the test observations, the parameters of the classic Burgers creep model are modified by considering the effect of normal stress, and a stress-dependent Burgers creep model is proposed. The proposed model includes eight parameters that can be conveniently calibrated using laboratory tests. A comparison of model predictions and test data for saturated Neogene red clay is performed to validate the model performance in describing the stress-dependent creep behaviour. The discussion provides an explanation for the creep mechanism of the loess–Neogene red clay landslide in terms of the stress-dependent creep behaviour of saturated Neogene red clay.