Abstract: Incorporating array of metallic wires into the host media, such as ferrimagnet YIG under an external magnetic bias field, is a novel method to synthesize negative refractive index (NRI) material. A modified effective medium theory of composite medium permittivity tensor is deduced. In our theory, the composite medium in the mass are transformed into an equivalent media that both permeability and permittivity are anisotropic. The effective permeability and permittivity tensors are calculated, the dispersive curves are presented, and the negative refractive condition is obtained by analysis.