In the experimental study on the creep characteristics of soil, the drained creep experiments are seldom performed due to the restriction of the experimental condition. Even less effort is made to first retrieving the initial consolidation conditions and then conducting the triaxial drainage creep characteristic tests. In this stuy, consolidation creep test is performed in two stress paths including axial loading and lateral unloading to investigate the creep characteristic of saturated silt soil. Based on the experimental results, some conclusions are drawn as follows. First, the axial creep characteristics for the two stress paths are consistent under the drainage conditions, though the volumetric strain is much smaller than the axial strain, and the volumetric strain shows alternating shear shrinkage and shear dilatancy when time elapses. Based on the three-unit mechanical model, the creep starting time of the oozy soil is estimated as 100-200 min after applying the deviatoric stress during the creep test. The creep coefficient of the oozy soil is defined and its variation is characterized. It is found that the creep coefficient is closely related to the deviatoric stress level, i.e., regardless of confining pressure and loading path, creep coefficient increases linearly with deviatoric stress level, and is not influenced by such factors as the initial consolidation confining pressure, load applying way, etc. Finally, it is proposed that the NHRI model describing the transient elastoplastic strain be combined with the creep empirical formulation describing creep strain, so that a creep constitutive model can be developed.