Abstract: We designed a double negative medium structure for 12.5 GHz based on the principle of negative dielectric constant and permeability, using metal wires and a split ring resonator. The S-parameter was calculated in special boundary conditions. Equivalent parameters were obtained by using the Nicolson-Ross-Weir method. We achieved the characteristics of the left-handed material, that is that the dielectric constant, permeability and refractive index were all negative and the refractive index approximately zero. The double negative medium structure was optimized numerically which applied in Ku-band cone horn antenna. Antenna gains were improved from 11 GHz to 13 GHz and increased 2.17 dB at 12.5 GHz. In the experiments, the antenna gain increased 1.51 dB with the double negative medium loaded, and simultaneously the backward radiation decreased 5.7 dB. The radiation characteristics were improved obviously.