In this paper, the microstructure and the dielectric properties of Sr$\_$1-x/CaxTiO$_3$(0$leq$x$leq$0.2)-based grain boundary layer ceramics were investigated. The sintering temperature and time were 1420∼152 0$^{C}$ and 4 hours in N$_2$ gas, respectively. The average grain size and the lattice constant were decreased with increasing content of Ca, but the average grain size was increased with increase of sintering temperature. The second phase foamed by the thermal diffusion of CuO from the surface leads to verb high apparent dielectric constant, $xi$$\_$r/>50000 and low dielectric loss, tan$delta$<0.05. X-ray diffraction patterns of Sr$\_$1-x/CaxTiO$_3$ exhibited cubic structure, and the peaks shifted upward and the peak intensity were decreased with x. This is due to the lattice contraction as Sr is replaced by Ca with a smaller ionic radius. The specimens treated thermal diffusion for 2hrs in 1150$^{C}$ exhibited nonlinear current-voltage characteristic, and its nonlinear coefficient(a) was overt 7.