<p>Layered rocks, widely distributed in highway and railway tunnels, exhibit significant transversely isotropic creep properties, resulting in significant time-dependent unsymmetric convergence and unsymmetrical pressure on linings. This study proposes a transversely isotropic nonlinear viscoelastic–viscoplastic model to accurately describe the creep behavior of layered rocks at various bedding angles using a single set of model parameters, established by coupling a standard solid model and a nonlinear damage viscous element in series. Taking into account the influence of bedding microstructure, the creep compliance of the standard solid model is introduced in the stress–strain relationship in global coordinates using the compliance substitution method to obtain the viscoelastic constitutive equation of the proposed model. The Mohr–Coulomb plastic criterion is modified by a microstructure tensor approach to describe the transverse isotropy observed in cohesion and friction angle and extended to a Mohr–Coulomb (MC) type viscoplastic criterion, with which the viscoplastic constitutive equation of the proposed model is derived based on the over-stress theory. The validation and comparison analysis of the proposed model indicates that this model effectively captures the viscoelastic–viscoplastic deformation characteristics of layered rocks across various bedding angles with remarkable precision, requiring only a singular set of parameters. Furthermore, the influence of anisotropic structural parameters, deviatoric stress, bedding angle, and confining pressure on the proposed model has been thoroughly analyzed, and the analysis reveals that the reliability of the proposed model remains robust across varied loading stress states.</p>