Since ultra-high dielectric constants (>104) with weak temperature and frequency dependence were observed in non-ferroelectric materials such as CaCu3Ti4O12and CuO, it is very meaningful to study the dielectric properties not only of CaCu3Ti4O12and CuO, but also of other members in the CaO-CuO-TiO2system in order to find other compositions with similar characteristics, to discover the underlying mechanisms and to search for new composites with even better dielectric properties. The dielectric properties of the composites in ternary systems CuO-CaCu3Ti4O12-CaTiO3and CaCu3Ti4O12-CaTiO3-TiO2have been tentatively investigated in the present study. The frequency and temperature dependences of permittivity and impedance in the range of 102-5x106Hz and 25-130 °C were investigated in the representative high permittivity (>104) composite with molar fraction of Cu/Ti/Ca of ~85/10/5 in the ternary system CuO-CaCu3Ti4O12-CaTiO3. Strong hints suggest an important effect of grain boundary contributions on dielectric properties. Preliminary results demonstrated that a multiphase microstructure consisting of larger grains with predominant phase surrounded by smaller grains with secondary phases played an important role for enhancing the dielectric response due to possible barrier layer effects caused by the grain boundary of the composites.