In this work, two groups of single domain YBCO grains with c-axis perpendicular (Pe-Y123) and parallel (Pa-Y123) to the top surface, were fabricated by the RE + 011 TSIG method under different supercooling temperature (ΔT). The effect of ΔT on the a-axis and c-axis growth rates on the surface (Ras and Rcs) and interior part (Rai and Rci) of YBCO grains were systemically investigated, and the magnetic levitation properties of single domain YBCO bulk superconductors were studied. The results indicated that the top surface morphology exhibits square shape for Pe-Y123 group bulks and rectangular shape for Pa-Y123 group bulks. All growth rates increase nearly linear with the rising ΔT. Ras and Rcs are greater than the Rai and Rci, respectively. Both Rcs and Rci are greater than Ras and Rai under the same ΔT. Pe-Y123 superconductor is of greater levitation force, while Pa-Y123 superconductor is of relatively higher guidance force. These results are very helpful for understanding the crystal growth difference between the surface and internal of the single domain YBCO bulks, and provide a new way to fabricate REBCO bulks with designed grain orientation for different applications.