The long-term deformation and permeability evolution with time are key issues for geo-engineering applications such as radioactive waste disposal. Rock permeability concurrent with deformation is significantly influenced by cracking. This study investigated the creep-permeability evolution behavior of red sandstone specimens containing a single fissure under a confining pressure of 30 MPa. First, the effects of stress ratio (SR) and fissure dip angle on the creep behavior of rock were investigated. The more loading/unloading cyclic numbers, the larger the irrecoverable axial deformation. The instant elastic strains and visco-elastic strains linearly increased with SR for both the intact and fissured specimens, whereas the instant plastic strains showed different results. The visco-plastic strains nonlinearly increased. For fissured and intact specimens, the creep strains and the steady-state creep rates nonlinearly increased as SR increased. The instantaneous strains, instant elastic strains, and visco-elastic strains slightly varied when the fissure dip angle was less than 45° but notably decreased with increasing fissure dip angle beyond 45°. However, the fissure dip angle had no obvious effects on the plastic and creep strains. Damage (D) was defined using the ratio of non-elastic strains to the total strain. D increased approximately linearly with SR, but the fissure dip angle had no obvious influences. Subsequently, the long-term strength (LTS) of the red sandstone was determined using two different methods. The LTS first decreased when the fissure dip angle increased from 0 to 45° but increased with increasing dip angle. The triaxial and creep failure modes were mainly shear along anti-wing cracks for the fissured specimens but shear failure occurred for the intact specimen. Moreover, the permeability of the fissured red sandstone was governed by SR and deformation or time. During the multi-step loading/unloading creep process, the permeability first decreased and then had a sudden rise when tertiary creep occurred.