Understanding the damage evolution and time-dependent property of rock creep is of great significance for predicting geohazards and evaluating the long-term stability of geotechnical structures. In this study, a three-dimensional digital image correlation system was adopted to investigate the creep behavior of sandstone under the coupling action of stress and pore water pressure. The apparent strain fields, deformation characteristics of the localization zone, and micromorphology of the fracture surface were analyzed. The results demonstrated that when the applied deviatoric stress level was above σci (crack initial stress) or σcd (crack damage stress), the increase in pore water pressure promoted creep deformation evidently, improved the creep rate significantly and shortened the time-to-failure of the rock obviously. In the radial strain field, the localized development of substantial microcracks on the rock surface was concentrated in the steady-state creep, while the microcracks interconnected to form macroscopic shear cracks that dominated the accelerating creep, and this damage evolution characteristic can be used as a precursor and early warning of rock creep failure. Besides, increasing the pore water pressure also would cause the divergence point of strain curves inside and outside the localization zone to appear earlier at the secondary creep, and produce a wider localization zone at the tertiary creep. The creep fracture surface of the rock was dominated by intergranular microcracks. Increasing the pore water pressure would result in the deterioration of the cemented structure and breakage of the cemented matrix more seriously, thus stimulating the generation of more microcracks.