The shear stress relaxation of the anchor-soil interface is the key factor causing the prestress loss of anchor rod (cable). Firstly, a device for testing the shear stress relaxation of the anchor-soil interface was developed. Secondly, a constant interface shear displacement was applied in stages to the red clay anchored element sample, and the whole process of shear stress relaxation curve of anchor-soil interface was obtained, which can be transformed to the relaxation curve at each specific loading level by using coordinate translation method. Then, the theory of fractional calculus was introduced to improve the viscous pot element, and established the red clay-anchor grout interface shear fractional M||N (composed of Maxwell body and Newton body in parallel) relaxation model. The model parameters were yielded by regression analysis of relaxation test curves under partial shear displacements, and the relationship between the model parameters and the shear displacements was also obtained by fitting. Finally, the established fractional M||N relaxation model was applied to predict another part of the relaxation curve under shear displacement level. By comparing the integer-order M||N model, the Burgers model and the five-element model (H||M||M), the results indicate that the proposed fractional M||N relaxation model not only has the advantages of simple structure and fewer parameters, but also has higher fitting and prediction accuracy.