In order to explore the application of the dielectric properties of white matter and grey matter in β, δ and γ dispersion transition zones used in clinical medicine and microwave imaging technology, we calculated the dielectric constant and its increment by using Cole-Cole equation. Based on the mutation of the increment of dielectric constant, the frequency range of three dispersions were evaluated. The dominate dispersion and the corresponding polarization mechanism were analyzed by using Cole-Cole circle. The results showed that there are 3 transition zones in brain white matter, which occur between β and δ dispersion, δ and γ dispersion and β and γ dispersion respectively. In grey matter, there are only 2 transition zones, which are between β and δ dispersion and δ and γ dispersion respectively. By comparing the frequency range of white matter and grey matter, the frequency range in white matter is broader than that in grey matter for the transition zone of β and δ dispersion with the β dispersion occupying dominate position in both tissues, and the corresponding polarization mechanism is interfacial polarization. For the transition zone of δ and γ dispersion, the frequency range in white matter is also broader than that in grey matter with the δ dispersion occupying dominate position in both tissues, and the corresponding polarization mechanism is orientation polarization. This study can provide basic theory and reference for diagnosis of brain diseases and microwave imaging technology.