The layered surrounding rocks of deep tunnels undergo large creep deformation due to the presence of planes of weakness and the presence of prolonged high in-situ stress, thereby the deformation severely endangers the safety of tunnels. This study conducts uniaxial compression creep tests to experimentally investigate the transversely isotropic creep characteristics and the damage mechanism of layered phyllite samples having bedding angles of 0°, 22.5°, 45°, 67.5°, and 90°. The results indicate that the creep deformation of the specimens takes place in four stages: the instantaneous elastic deformation stage, the deceleration creep stage, the steady-state creep stage, and the accelerated creep stage. The cumulative creep deformation and the creep time during the steady-state creep stage of the specimens initially decrease and then increase as the bedding angle changes from 0° to 90°, thereby, corresponding to the initial increase and subsequent decrease in creep rate during the deceleration creep stage. Based on the existing viscoelastic-plastic damage creep model, the creep parameters E1, E2, η2, and η3 are observed to initially decrease and then increase with the increase in bedding angle, hence demonstrating that the creep characteristics and damage mechanism of the layered rock mass are controlled by the effect of the natural weakness planes and show significant transversely isotropic characteristics.