We investigate the effective refractive index n e of a granular composite, in which metallic magnetic inclusions having dispersive permittivity and permeability are embedded in the host medium. By taking into account the dipole interactions between the spherical granulae and the relative size of the internal wavelength, we develop the Clausius–Mossotti approximation to investigate the effective refractive index spectra of the composite. The results show that for a given volume fraction larger than a fraction threshold p t , the whole composite can be left-handed in a finite frequency region, characterized by the negative refractive index. At a certain frequency ω c , there exists a negative index valley, whose magnitude exhibits nonmonotonic behavior, along with ω c being shifted to the long-wavelength with increasing p. The frequency-dependent cancelling volume fraction p c , defined as the one at which Re( n e )=0, is predicted. Furthermore, a three-component system with separate inclusions for electric and magnetic properties is also investigated.