The complex dielectric constant has been measured for a polyvinyl-ether based cyano-biphenyl side-chain liquid-crystalline polymer over the temperature range of 100-400 K and frequency range of 10-10(5) Hz. In the smectic-A phase, both homogeneous and homeotropic alignments were achieved with a 7-Tesla magnetic field by slowly cooling the samples down from the isotropic phase to room temperature. The low-frequency delta loss peaks are suppressed in the homogeneous state and enhanced in the homeotropic state while high-frequency alpha loss peaks are enhanced in the homogeneous and almost absent in the homeotropic. The Arrhenius plot of each process shows a rapid decrease in the relaxation frequency as the temperature approaches T(g), which may somehow reflect the glassy behavior of the polymer backbone and has been analyzed by WLF and Vogel-Fulcher equations. The results from two samples with different degree of polymerization are compared in terms of T(g).