Based on the geometric quantum discord measurement method proposed by Dakic, the geometric quantum discord of double Jaynes-Cummings (J-C) model is investigated. Influences of the initial state purity, entanglement degree, coupling constant between atom and cavity, intracavity photon number on the evolution characteristics of geometric quantum discord with time are analyzed. Results show that geometric quantum discord can be increased by increasing the purity and initial entanglement value. The non-zero photon number leads to the decay of geometric quantum oscillate oscillate. The oscillation frequency can be changed by adjusting the coupling constant between the atom and cavity.