The (Sr$_{1-x}$ .Ca$_{x}$)TiO$_{3}$(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). After being fired in a reducing atmosphere, 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. The results of the capacitance-valtage measurements indicated that the grain boundary was composed of the continuous insulating layers. The capacitance is almost unchanged below about 20[V], but decreased slowly over 20[V]. The conduction mechanism of the specimens observed in the temperature range of 25~125[.deg. C], and is divided into three regions having different mechanism as the current increased: the region I below 200[V/cm] shows the ohmic conduction. The region II 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.ct.