The geometrical quantum discords betwe en two subsystems in the coupled-cavity system are studied when there are the a tom-decay and the cavity-decay.Under the special condition that atomic decay r ate equals to the decay rate of cavity field,the evolution of the system state v ector is given.The effects of the atom-decay and the cavity-decay on the geome trical quantum discords are discussed.Numerical results show that the geometrica l quantum discords between two atoms,between two cavities,as well as between ato m and cavity all exhibit damping oscillation behavior until they decay to zero.O n the other hand,the decays of these geometrical quantum discords are all accele rated with the increase of decay rate.