we fabricated large single grain YBa$_2$Cu$_3$O$_{x}$ (Y-123) superconductors. The single grain Y-123 was grown by top seeded melt growth (TSMG) method. In a conventional box furnace with uniform temperature distribution, it was very difficult to grow large single grain Y-123 superconductors due to the size limitation in growth. To overcome the size limitation, we applied a radial thermal gradient (lower temperature at sample center and higher temperature on the sample edge) to the TSMG process. In this case, large single grain Y-123 could be easily grown. This is attributed that the liquid of the sample edge was maintained at the high temperature compared to the growth front. Using this method, we successfully fabricated a large single grain Y-123 of 6.4 cm X6.4 cmcm