The influence of structural anisotropy on time-dependent behaviour of foliated metamorphic greenschist collected from deep underground tunnel (−1300 m) in China was investigated to acquire the fundamental knowledge of the long-term mobility of greenschist in nature. Considering the structural anisotropy, greenschist samples with different inclination of foliation/bedding planes (i.e., θ = 0°, 35°, 45°, 60° and 90°) was prepared for creep test. Multi-stage constant loading method is employed in this test with each stage equals to 10 MPa, 20 MPa, 30 MPa and 40 MPa respectively for presenting analogous situation of variable stressing of greenschist caused by over laying rocks and tectonic stresses. The test results revealed the significant effect of structural anisotropy on the creep development (i.e. instantaneous strain, transient creep, steady-state creep) and failure mode. The control of structural anisotropy on steady-state creep rate is strengthened at high stress level, compared to that is weaken on other properties (i.e. instantaneous strain, transient strain), which is mainly due to the evolution of tensile and shear crack along and cross the bedding plane at high stress level. The three types of failure models of greenschist (i.e. shear along the bedding plane, cross the bedding plane or compound) were observed which hints that the long-term mobility of greenschist rockmass is mainly dependent on characteristic of structural anisotropy and stress conditions. In addition, based on the experimental results, creep models were proposed for greenschist considering the bedding plane and their parameters were obtained using test result. We believe that these test results and the models would throw some insights and benefit practicing design engineers and numerical modellers.