A dielectric ceramic material composed of primary and secondary ingredients forming in combination a polycrystalline ceramic proper, and of insulating substances diffused throughout the intergranular boundaries of the ceramic proper for an increase in apparent relative dielectric constant. The primary ingredients comprise, in relative proportions, 95.18-99.65 wt. % SrTiO.sub.3, 0.33-3.32 wt. % Ta.sub.2 O.sub.5, and 0.02-1.50 wt. % CuO. The secondary ingredients comprise 0.02-0.10 wt. % part SiO.sub.2 and 0.01-0.03 wt. part Al.sub.2 O.sub.3 with respect to 100 wt. parts of the primary ingredients, with the weight ratio of SiO.sub.2 to Al.sub.2 O.sub.3 being from 1.50 to 5.0. The insulating substances comprise 0.03-2.75 wt. % PbO, 0.11-4.22 wt. % Bi.sub.2 O.sub.3, and 0.001-0.18 wt. % B.sub.2 O.sub.3 with respect to the total weight of the primary and the secondary ingredients. In the fabrication of bodies of the ceramic the mixture of the insulating substances is coated or otherwise layered on polycrystalline ceramic bodies prepared from the primary and secondary ingredients. The coated ceramic bodies are then heated to cause diffusion of the insulating substances throughout their intergranular boundaries.