The subsolidus phase relations of the ternary system CuO-TiO
2
-CaO sintered at 950 °C in air have been determined by powder X-ray diffraction method. Only one ternary compound CaCu
3
Ti
4
O
12
was found in this system. From room-temperature dielectric property mapping at 10 kHz, a giant dielectric constant (
ε
r
10
4
) was observed for most of the ceramic composites in the CuO-rich region and in the region along the CaO
-CuO binary line. The composites in the CaCu
3
Ti
4
O
12
-rich region were found to give a comparable giant dielectric constant when sintered at 1050 °C. The particular microstructure of larger grains with predominant phase surrounded by smaller grains with the secondary phases was found in such composites with a high dielectric constant. The relations between structures and dielectric properties were investigated. An internal barrier layer capacitance effect is the most probable mechanism to explain this particular dielectric behavior.