Zirconium alloys have been widely used because of their good mechanical properties, corrosion resistance, and suitable neutron absorption cross section. However, with the development of engineering technology, the requirements on the service performance, safety, and microstructure stability of zirconium structural materials are increasingly high. Creep refers to the phenomenon where the strain of the material increases with time under the action of stress lower than the yield strength, which will lead to the deformation of the structural material and eventually its failure. It is also an important problem faced by zirconium cladding materials in nuclear reactors. Nanocrystalline zirconium is a strengthening and toughening method, which may also improve other properties of nuclear materials. However, there are very few investigations on the microscopic creep mechanism in the atomic scale of nanocrystalline zirconium. Improving the creep resistance of zirconium materials plays an important role in the safety of components. Therefore, studying the creep behavior of nanocrystalline zirconium and its atomic mechanism is conducive to its better application in industries. In this study, the tensile creep behavior of nanocrystalline α-Zr under different conditions was investigated via molecular dynamics simulation. The main influencing factors of the creep process were analyzed and the influence of polycrystalline structure evolution and deformation mechanism during the steady-state creep process was studied. The effect of irradiation on the creep process was preliminarily explored. Results showed that temperature, stress, irradiation, and grain size affect the creep behavior of nanocrystalline α-Zr. Increasing the temperature and stress level and refining the grains can promote the creep process. The microstructure of the system changed significantly after the creep. Some grains grew up with the creep deformation process, while others gradually shrank, or even disappeared. During deformation, the lattice distortion gradually propagated from the grain boundary to the grains, partly reducing the degree of the hcp order. Simulation results showed that grain boundary migration is the main deformation mechanism of nanocrystalline α-Zr during steady-state creep. Increasing the temperature and stress level will thicken the grain boundary and promote the microstructure evolution. After the cascade collision due to neutrons of different energy levels, a large number of point defects were produced in the system and their diffusion contributed to the creep; these defects were finally collected at the grain boundary, improving the grain boundary mobility. Increasing the irradiation energy can increase the number and size of irradiation defects, promoting the creep process of the nanocrystalline system.