Relative complex permeability spectra (μr=μr′-iμr′′) and the dc magnetic field effect on them for a yttrium iron garnet (YIG) and its granular composite materials have been studied to evaluate the negative permeability characteristics. In the sintered YIG, two distinct peaks corresponding to the domain wall and the gyromagnetic spin resonance were observed in the imaginary part μr′′ under zero magnetic field; the real part of complex permeability μr′ shows a small negative value in a certain frequency range. The Lorentz type magnetic resonance with the negative permeability dispersion was observed under dc magnetic field. Permeability spectra were evaluated by the numerical fitting of actual measurement data to a resonance formula using six parameters (resonance frequencies, static susceptibilities, and damping factors of the domain wall motion and the gyromagnetic spin rotation). The dc magnetic field suppresses the domain wall contribution and the spin component becomes dominant. In the YIG granular composite material, the permeability dispersion frequency shifts to higher frequency region due to demagnetizing field; the spin component becomes dominant. Negative permeability spectra were also observed in the high content YIG composites under the dc field. The negative permeability spectra of YIG composite materials can also be applied to the left-handed material as well as the sintered YIG.