Abstract: The supercurrent in a Josephson junction composed of a zigzag-edged graphene nanoribbon (ZGNR) lying between two superconducting leads ［superconductor-graphene-superconductor (SGS) junction］ has been studied by the Green's function method. It is found that applying a small transverse electric field can reverse the supercurrent direction, leading to a so-called 0-π phase transition. This transition can also happen periodically with a given change in the ZGNR's length, and, more importantly, can be easily and electrically controllable by a gate voltage, which is not possible in conventional superconducting π junctions and makes the SGS junction very promising for future application in superconducting electronics, as well as in quantum information and computation.