Three kinds of GaN samples (hexagonal coarse-grain powders, hexagonal nanoparticles and cubic nanoparticles) were synthesized by different methods. The room-temperature frequency spectra of the relative dielectric constant and that of the dielectric loss were measured in the frequency range of 100 Hz to 10 MHz. Analysis of these spectra indicates that the grain size of samples has great influence on the dielectric behavior of samples whereas the crystallography symmetry almost has no impact on the relative dielectric constant.