Single crystals of the superconducting Y-Ba-Cu oxide were grown by a flux technique. Stoichiometric mixture with excess BaO and CuOcontent was melted at 130$0^{circ}C$, followed by fast cooling to 108$0^{circ}C$ to prevent crystallizing of CuO. It was then reheated to 110$0^{circ}C$ followed by being held at this temperature to control the number of nuclei, and cooled by 5$^{circ}C$/hr to 80$0^{circ}C$. This procedure was repeated with various compositions and crystals were obtained in cavity. Molten solution was seperated to two parts : the upper part of almost CuO and the rest of different composition. Appropriate composition of flux was 30mol% BaO and 70mol% CuO due to the seperation of molten solution. Single crystals have the habit of thin plate with good developed (001) crystal face, XRD, EDAX and single crystal X-ray investigations were carried out. The grown crystals have tetragonal structure with the lattice parameters a=b=3.84$AA$, c=11.7$AA$, and the space group P4/mmm. The crystal surface were observed by SEM.