Fluorinated graphene is one of the most important derivatives of graphene and has been found to have great potential in optoelectronic and photonic nanodevices. However, the stability of F atoms on fluorinated graphene under different conditions, which is essential to maintain the desired properties of fluorinated graphene, is still unclear. In this work, we investigate the diffusion of F atoms on pristine graphene, graphene with defects and at graphene/fluorographene interfaces by using density functional theory calculations. We find that an isolated F atom diffuses easily on graphene, but those F atoms can be localized by inducing vacancies or absorbates in graphene and by creating graphene/fluorographene interfaces, which would strengthen the binding energy of F atoms on graphene and increase the diffusion energy barrier of F atoms remarkably.