Disclosed is a method for producing a barium titanium oxide single crystal piece with a given structure using a containerless solidification process, which comprises the steps of preparing a material made of a barium titanium oxide, controlling the material to be in a levitated state within a levitation furnace, melting the levitated material using a laser, and solidifying the molten material while maintaining the levitated state. In a specific embodiment, a spherical sample having a composition of BaTiO3 and a weight of about 20 mg is subjected to a rapid solidification and melting process (temperature gradient: about 700 K/sec) 3 times while levitating the sample in 4.5 atm of air atmosphere using an electrostatic levitation furnace. Then, the re-molten sample is maintained at a temperature just below the melting point of the sample for a given time, and then rapidly cooled at a cooling rate of 300 K/sec to obtain a transparent blue barium titanium oxide single crystal. The single crystal exhibits innovative dielectric characteristics having a large relative permittivity (100,000 or more at room temperature) and a low dielectric loss. In addition, the single crystal has excellent temperature stability allowing the relative permittivity to be gently reduced in the range of room temperature to 70 K.