A wet solid-state method was used in this work to produce Ba0.97Bi0.02TiO3–Ba1−xMgxSn0.02Ti0.98O3 materials. By using core-shell structure nanocubic Ba1−xMgxSn0.02Ti0.98O3 (BMST) decorated Ba0.97Bi0.02TiO3 (BBT) assemblies, a composite capacitor with improved dielectric constant and enhanced breakdown strength was successfully fabricated in contrast with the composite ferroelectric Ba0.97Bi0.02TiO3–BaSn0.02Ti0.98O3 (BBT–BST) ceramic. With increasing Mg content, the ceramic capacitors display a stronger performance in its dielectric behavior. The best dielectric properties were obtained in the composition x = 0.007 with the dielectric constant above 65,000. The dielectric strength of the ceramics was measured by a withstanding voltage tester. The best dielectric strength was achieved in the composition x = 0.007 with E = 5.455 kV/mm.