Graphene attracts much attention in recent years due to its unique energy band structure and excellent electro-optical properties. One of the important researches is the graphene optical fiber which is consist of graphene and optical fiber. The structure and basic properties of graphene are introduced. Graphene, which is with a two-dimensional honeycomb lattice structure composed of single-layer carbon atoms which are formed by the close stacking of sp2 hybird orbital, shows excellent properties in machinery, electrology, optics and thermodynamics because of its unique energy band structure with zero band gap. The research progress of graphene-based optical fiber devices at home and abroad is briefly reviewed. The working principle and device characteristics of lasers, modulators, surface plasmon resonance sensors and polarizers based on graphene optical fiber are described. The current problems and future development trends of graphene optical fiber are analyzed.