Glasses on BaO-B2O3-Al2O3 and BaO-B2O3-Ga2O3 systems were grown by a new Floating-zone Pulling Down method. Grown glasses were transparent below 200 nm, and could be characterized from a viewpoint of composition dependence of third-order nonlinear optical properties, chi ((3)), at 355 nm. The value of chi ((3)) was two to three times larger than that of standard fused silica, and increased with the increase of Al2O3, Ga2O3, and BaO amount.