Dielectric behavior of a typical liquid crystal polymer Vecstar was studied by measuring its dielectric permittivity, conductivity and other electrical properties. Dielectric spectra are analyzed combined with the thermal properties and thermally stimulated current spectra, and space charge distributions. Complex electrical modulus is introduced in the analysis of the permittivity spectra, which proves to be effective to suppress the effects of large conduction currents at high temperatures. Moreover, the slope of the frequency dependence of εr' is different below and above 160 oC, which indicates that the Maxwell/Wagner polarization occurs inside the sample. The experimental results indicate that both the dielectric relaxation and electrical conduction are closely related with molecular motion and phase transition of the polymer. It is also shown that the polymer is an excellent insulating material in a wide temperature and frequency range.