High temperature creep in nickel-based superalloys is investigated by discrete dislocation plasticity (DDP). A two-dimensional unite cell model representing micro-structure of superalloy and comprising γ^' particles in γ matrix phase is considered under uniaxial constant stress loading. While plastic deformation of γ phase occurs by a combination of dislocation glide and dislocation climb coupled to the diffusion of vacancies, elastic γ^' particles undergo deformation due to the stress-driven interfacial diffusion at the γ/γ^' interfaces in addition to bulk elastic deformation. It is noted that diffusion of vacancies is explicitly considered where local concentration of vacancies determines climb of dislocations. This model predicts the onset of tertiary creep in superalloys as extensively observed in experiments for commercially important nickel-based superalloys at moderate stress and temperature levels. Possible associated mechanisms are accordingly discussed. Moreover, effects of parameters such as volume fraction of γ^' particles are studied and discussed. Superalloys with three values for volume fraction of γ^' particles are investigated and obtained results indicate that the volume fraction of γ^' particles plays an important role in the creep behaviour of superalloys. Results of this study can be used in a continuum constitutive rule to investigate structural components under operational conditions.