Large bulk HTS single crystal can be used to measure accurately the structure and understand the relation between crystal structure and properties, as well as to obtain more information on its nature for high Tc superconductor. It is important to understand and explain the mechanism of high Tc superconductivity and their applications. It is quite difficult to obtain a large bulk HTS single crystal due to peritectic reaction, peritectic transformation and incoordinate composition transformation in the crystal growth process of HTS oxides, especially, a liquid-solid line of steep slope in YBCO phase diagram. Crystal growth theory related to HTS single crystal grown and techniques, some effects and improvements for crystal growth were discussed in this paper. In addition, some techniques for preparing HTS single crystal were summarized.