The (Sr$_{1-x}$ .Ca$_{x}$)TiO$_{3}$+0.6[mol%]Nb$_{2}$O$_{5}$ (0.05.leq.x.leq.0.2) ceramics were fabricated to form semiconducting ceramics by sintering at about 1350[.deg. C] in a reducing atmosphere(N$_{2}$ gas). Metal oxides, CuO, was painted on the both surface of the specimens to diffuse to the grain boundary. They were annealed at 1100 [.deg. C] for 2 hours. The 2nd phase formed by thermal diffusing from the surface lead to a very high apparent dielectric constant. According to increase of the frequency as a functional of temperature, all specimens used in this study showed the dielectric relaxation, and the relaxation frequency was above 106 [Hz], it move to low frequency with increasing resistivity of grain. The specimens showed three kinds of conduction mechanisms in the temperature range 25-125 [.deg. C] as the current increased: the region I below 200 [V/cm] shows the ohmic conduction. The region rt between 200 [V/cm] and 2000 [V/cm] can be explained by the Poole-Frenkel emission theory, and the region III above 2000 [V/cm] is dominated by the tunneling effect.fect.