Diffusion controlled creep in nanostructured materials is considered for the case when grain growth occurs concurrently. The Nabarro-Herring and Coble mechanisms that would predict creep rate reduction are re-considered to include the effect of grain-growth induced vacancy generation. It is shown that under such conditions creep is accelerated during an initial stage of grain growth as compared to the case of constant grain size. This creep enhancement stage is followed by a period of reduced creep rate. The predicted strain rate behaviour resembles primary and secondary creep.