The cavity each imprisons one two-level atom,the atom has a resonant interaction with the cavities,and the cavities also interact with each other. Considering these,the geometrical quantum discord was used to measure quantum correlation in quantum systems. The geometrical quantum discord between the atoms,the cavities,and also between the atoms and the cavities were investigated. By using the numerical method,the evolution curves of the geometrical quantum discord were given,and the influences on the geometrical quantum discord with the changing coupling constant between the cavities were discussed. The results obtained show that the geometrical quantum discord between atoms is strengthened,but the geometrical quantum discord between cavities or between the atoms and the cavities are all weakened with the increasing of the coupling constant between cavities.