To meet the application requirements under complex service conditions for aero engine blades, the influence of stress-state on creep behavior of a self-designed Re-low Ni-based single crystal superalloy at 1038 °C over a wide stress range of 137–207 MPa was investigated. With applied stress decreasing from 172 to 137 MPa, the creep life rapidly extends by a factor of 2.41, showing strong stress dependence. Further, the creep mechanisms under different stresses are discussed based on microstructural characterization and threshold stress calculation results. With the increasing applied stress, interfacial dislocation networks exhibit sparse and irregular shapes. Particularly, in necking zone of the fractured specimen at 1038 °C/137 MPa, due to the long-duration accumulation of deformation storage energy, dislocation arrays within γ′ rafts gradually evolve into dislocation walls through recombination and annihilation of dislocations, then develop into subgrain boundaries. Finally, some recrystallization grains with large misorientations (>10°) form by subgrain-rotation. Moreover, based on the calculated threshold stress, dislocations climbing can play a major role in creep deformation throughout the steady-state stage under a stress range of 137–207 MPa. Nevertheless, with the arrival of tertiary stage, the increasing actual stress resulted from necking deformation can also promote dislocations to cut or bypass γ′ rafts under lower stresses (137 and 172 MPa), which is consistent with the final evolution of dislocation substructures. Overall, the findings from this work are helpful to understand the high-temperature creep mechanism of low-cost single crystal superalloys, so as to improve the creep resistance of materials.