Microstructures and dielectric properties of (Sr$\_$1-x/Ca$\_$x/) TiO$_3$-0.006Nb$_2$O$\_$5/ (0.05$leq$x$leq$0.2) boundary layer ceramics were investigated. The samples fired in a reducing atmosphere(N$_2$) were painted on the surface with CuO paste for the subsequent grain boundary diffusion, and then annealed at 1100$^{circ}C$ for 2 hrs. The metal oxide of CuO infiltrated by thermal diffusion from surface of sample presents continuously in not grain but only grain boundary, and makes up thin boundary phase. The SEM photo, and EDAX revealed that CuO was penetrated rapidly into the bulk along the grain boundaries during the annealing. The average grain sizes is continuously increased as the content of substitutional Ca is increased from 5[mol%] to 15[mol%], but the average grain size of the sample with content of 20[mol%] Ca is slightly decreased. In the samples with content of 10∼15[mol%] Ca, excellent dielectric properties were obtained as follows; dielectric constant <25000, dielectric loss <0.3[%], and capacitance change rate as a function of temperature <${pm}$10[%], respectively. All samples in this study exhibited dielectric relaxation with frequency as a functior of the temperature.