The shear constitutive model of soils plays a key role in the stability analysis of slopes. In this work, a statistical damage-based shear constitutive model for soils and its parameter determination method are proposed. An improved Weibull distribution function is introduced to calculate the damage variable. The shear test results of the slip band soils of the three gorges reservoir area in China are used to validate the proposed model. Quantitative indexes such as coefficient of determination, mean absolute percentage error and mean square error confirm that the accuracy of the proposed model is higher than that of an existing model. Compared with the existing model, the proposed model can better describe the experimental curve of shear stress vs. shear displacement in the post-peak stage. To analyze slope stability, a displacement-dependent transfer coefficient method is proposed by combining the proposed shear constitutive model with limit equilibrium theory. A case study demonstrates that the soil deformation at both ends of the slide mass is in the strain softening state first as the external load increases, and the resisting segment of the slide mass is located in its middle position. For a specified factor of safety, by considering the strain softening behavior in the proposed method, the computed allowable displacement of the slope is reduced at most by approximately 27% to that using the existing method neglecting the characteristics. The displacement-dependent transfer coefficient method reflects the progressive failure mode of the slope and can easily determine the displacement mapped to a factor of safety varied with the slope stress state.