Microtwinning is the dominant creep deformation mechanism of nickel-based superalloy in certain temperature and stress conditions. This study proposes a novel temperature-dependent creep constitutive model based on microtwinning mechanism, which includes the glide of 1/6<112> partial dislocations and atomic diffusion in γ′ precipitates. Both microtwinning and anti-phase boundary shearing mechanisms are considered in the crystal plasticity finite element model. The numerical steady-state creep rates of single crystal and polycrystalline nickel-based superalloys agree with the experimental data at different holding stresses and temperatures. Microtwinning is activated at a lower stress than that of anti-phase boundary shearing. The competition between dislocation slip and atomic diffusion is analyzed, and the dominant mechanism is revealed for the microtwinning dominated creep at different holding stresses and temperatures. This study deepens the understanding of microtwinning-based creep deformation and could provide an effective model for the creep of nickel-based superalloy.