The Geometrical Quantum Discord (GQD) is an effective measure of quantum correlation in quantum systems. The system of W-like states atoms interacting with three coupled cavities connected by two optical fibers was investigated. In the case of like-W state, optical cavities and fiber field are all in vacuum state initially. The evolution of the state vector of the system is given. GQD is adopted to quantify the degree of quantum discord between atoms. The GQD dynamics between atoms are discussed. The influences of coupling constant between cavity and fiber on geometrical quantum discord between atoms are discussed. The results show that GQD between atoms is strengthened with increasing of coupling constant between cavity and fiber.