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In this paper, a novel approach is presented to synthesize microwave medium of negative refractive index by incorporating metallic wire array with negative effective permittivity into the host media such as ferrimagnet-YIG (yttrium iron garnet) applied by external magnetic field whose permeability is negative. We have designed the composite medium having negative refractive index in C/X band frequencies, analyzed and simulated its electromagnetic (EM) properties by use of EM EDA package based on time-domain finite integration method. The simulation results show that: ① the effective permittivity of the designed metallic wire array is negative in the frequency range from 7.02 GHz to 9.80 GHz; ② the permeability of YIG substrate immersed into an external magnetic field is negative in the frequency range from 5.22 GHz to 8.14 GHz; ③ EM wave can pass through the composite medium synthesized by the above designed metallic wire array and YIG substrate, and ④ the negative refraction behavior occurs on the interface between the composite medium and the normal material with positive refractive index in 7.51-8.13 GHz frequency range, in which the effective permittivity of the metallic wire array and the permeability of YIG substrate are negative simultaneously. The full wave simulation has demonstrated that the effective refractive index of the designed composite medium is indeed negative and ascertained that the proposed approach to design microwave medium with negative refractive index is viable.