Joints are the boundary that controls slope failure of rock slope. Most of the joints are non-persistent and embedded in the rock slope. The creep mechanism of non-persistent joints is of great significance to reveal the creep deformation behavior of the slope over time. However, the embedded non-persistent joints are difficult to sample and to replicate uniformly in large numbers. In the study, a modeling method for embedded non-persistent joints is proposed, and the shear creep test on embedded non-persistent joints was conducted. Based on uniaxial compression testing and shear creep testing, the phase characteristics of creep testing are analyzed, a nonlinear viscous acceleration element and damage variable suitable for structural surfaces are introduced, and a shear-creep-damage constitutive model for non-persistent joints is established. Three-dimensional shear creep constitutive equation is derived using the Laplace transform. Furthermore, Levenberg-Marquardt (L-M) algorithm and global optimization method are used to identify the creep curves and solve the model parameters. After identification and comparison of experimental results and model fitting results, the new constitutive model can clearly reflect the creep characteristics of the non-persistent joints, which provide reference for deformation characteristics of non-persistent joint rock slopes.