The conduction mechanism of polymer nano-composite electrolytes are studied using broadband dielectric spectroscopy over a wide range of frequency and temperature. The polymer nano-composites consisting of polyethylene oxide as polymer host, lithium trifluoromethanesulfonate as salt, and nano-crystalline zirconia as filler are prepared using solution casting method. Formation of polymer salt complex and nano-composites are confirmed from x-ray diffraction studies. The electrical conductivity and relaxation phenomena of the polymer salt complex as well as the composites are studied using broadband dielectric spectroscopy. At room temperature, the dc conductivity of the polymer nano-composites are found higher by two orders of magnitude than that of corresponding polymer salt complex. Temperature dependence of dc conductivity is following Vogel-Tamman-Fulcher trend, suggesting strong coupling between ionic conductivity and segmental relaxation in polymer electrolytes. Relaxation phenomena are studied with dielectric and modulus formalism. Frequency dependent ac conductivity show universal dielectric response and nearly constant loss features at high and low temperature regions respectively. The origin of universal dielectric response and nearly constant loss are analysed and discussed using different approaches. Kramer - Krönig approach suggests the origin of nearly constant loss is due to caged ion dynamics feature.