We demonstrate a nonsymmetrical composite metallic structure with realistic material parameters. This structure can realize double magnetic responses in near-infrared (NIR) range (0.92 mu m) and in visible range (0.61 mu m), which can be attributed to two different modes of magnetic coupling. The difference of the index dependence of two magnetic responses is due to the influence of metal on LC model at optical frequencies. The multimode magnetic responses may provide us a new way to design special nano-optical devices at high frequencies. We also show that magnetic response has larger sensitivity to the local index of dielectric than plasmon resonance and suggest a possible approach in detecting the local index of the dielectric surrounding metamaterials.