Geometric quantum discord as well as dense coding capacity were investigated in a model where two superconducting charge qubits were coupled with a Josephson junction. The influence of the initial mean photon number, relative phase and amplitude of the two qubits on the time evolution of geometric quantum discord and the dense coding capacity was discussed. The results show that the initial mean photon number, relative phase and amplitude of two qubits may play an important role in the evolution of geometric quantum discord and the dense coding capacity. Importantly, the dense coding channel capacity can be increased via changing the relative phases.