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Understanding the long-term creep mechanical behavior of granite is critical to evaluating the safety of the nuclear waste repository. It is unreasonable to extrapolate the creep test results of hard rock samples at high stress to lower stress. In this work, the uniaxial creep test of granite lasting for 1117 days is carried out at lower axial stress levels (60 and 87 MPa) to reveal its long-term time-dependent deformation characteristics. The test results show that under 60 MPa and 87 MPa, the creep deformation of granite accounts for only 21.7% and 36% of the total deformation, while that of salt rock is about 80%, making the creep of hard rock difficult to be detected. The steady creep rate of granite is 9.14 × 10−12 s−1, which is 1–2 orders of magnitude slower than that of salt rock under low stress, and 3–6 orders of magnitude slower than that under short-term granite creep test. At the same stress ratio of about 0.45, it takes 47.6 days for granite samples to enter the steady creep stage, which is much shorter than 213 days for salt rock samples. In the short-term (several hours or days) creep test under low stress level, the hard rock sample does not actually enter the steady creep stage. Based on the fractional derivative theory and damage mechanics, a novel nonlinear creep-damage constitutive model that can well describe the long-term brittle creep characteristics of granite is proposed. This research reveals the very long-term time-dependent deformation behavior of hard rock, which is conducive to the evaluation of long-term stability of nuclear waste repositories. [ABSTRACT FROM AUTHOR]