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In this work, the dielectric and non-Ohmic properties of $Ca_2 Cu_2-x Ge_x Ti_4 O_12$ ($CaCu_3Ti_4O_12$/$CaTiO_3$ composite) ceramic with additions of $GeO_2$ (x = 0, 0.025, 0.050 and 0.100) were prepared using a solidstate reaction method. X-ray diffraction technique was used to confirm the second phases of CaCu3Ti4O12 and CaTiO3 phases was detected in all the ceramics. The slight decrease in the grain sizes of $Ca_2 Cu_2-x Ge_x Ti_4 O_12$ ceramics can be observed using a scanning electron microscopy. The results revealed that ceramics sintered at 1060 °C for 6 h exhibited slightly different dielectric permittivity (~ 1784 – 2645), and the dielectric loss tangent was still very low (~ 0.036 – 0.018) at 1 kHz. This should be associated to insulating grain boundaries with activation energies of 0.80 eV by substitution of $Ge^(4+)$ for x = 0.050. The electrical responses of grains boundaries and internal interfaces were investigated using impedance spectroscopy. Strongly enhanced dielectric responses and variation in nonlinear electrical properties can be well described based on the electrical responses at internal interfaces of the ceramic composites.