The geometrical quantum discord (GQD) is an effective measure of quantum correlation in quantum systems. We have studied GQD dynamics of the system comprising two two-level atoms resonantly interacting with two coupled cavities. GQD between atoms and that between cavities are investigated. The influences of coupling constant between cavities and initial entanglement between atoms on GQD are discussed. Results obtained using a numerical method show that GQD between atoms is strengthened, and GQD between cavities is weakened with increasing initial entanglement between atoms. On the other hand, the evolution regularity of GQD between atoms and that between cavities are all strengthened with increasing coupling constant between cavities.