Geometrical quantum discord (GQD) is an effective measure of quantum correlation in quantum systems. We study GQD dynamics in an atom-cavity-fiber system. GQD between atoms and that between cavities are investigated. The influences of coupling constant between cavity and fiber and the intensity of the cavity field on GQD are discussed. Results show that GQD between atoms and that between cavities all display periodical evolutions, and their evolution frequencies increase with increasing coupling constant between cavity and fiber. On the other hand, the GQD between atoms and that between cavities are all strengthened with increasing intensity of the cavity field.