The results of measurements of dielectric constants, in the vicinity of ambient temperature, are presented for eight barium titanium niobium oxides (BaTi1+2nNb4O13+4n for n = 0, 1, 2, 3, 4; Ba3Ti4Nb4O21, Ba3Ti5Nb6O28, and Ba6Ti2Nb8O30) in polycrystalline ceramic form. The dielectric constants are in the range of 30 to 70. The results of dielectric measurements on solid solutions obtained by partial substitution of Ta for Nb are also reported. These substitutions do not dramatically increase the dielectric constants. One material, Ta-substituted Ba3Ti5Nb6O28, has a very low temperature coefficient of dielectric constant at K ≈ 45.