Various dielectric materials for millimeter wave planar circuits have been developed in Japan. In the developments of new substrate materials, it is necessary to evaluate the complex permittivity of them in the millimeter wave region. The developers hope that the new materials can be applied for various systems, such as 5G system, millimeter wave radar systems, and so on. Therefore the evaluation should be done at the wide frequency band in the millimeter wave region. Whispering gallery mode resonator method is applicable to evaluate the frequency dependence of the complex permittivity of low-loss dielectric materials in millimeter wave region. Furthermore, this technique is available for evaluations of the uniaxial anisotropy in complex permittivity, which appears frequently in the circuit board materials. In this presentation, the results of permittivity evaluations for some dielectric substrates by this WG mode resonator method will be shown and be discussed on validity of this method.