Graphene, a single layer of carbon atoms bonded in a hexagonal lattice, is the thinnest, strongest, and stiffest known material and an excellent conductor of heat and electricity. However, these superior properties have yet to be realized for graphene-derived macroscopic structures such as graphene fibers. We report the fabrication of graphene fibers with high thermal and electrical conductivity and enhanced mechanical strength. The inner fiber structure consists of large-sized graphene sheets forming a highly ordered arrangement intercalated with small-sized graphene sheets filling the space and microvoids. The graphene fibers exhibit a submicrometer crystallite domain size through high-temperature treatment, achieving an enhanced thermal conductivity up to 1290 watts per meter per kelvin. The tensile strength of the graphene fiber reaches 1080 megapascals.