This study investigated the phase transformation of the REBa$_2$Cu$_3$$O_{7-x}$ (RE=Nd, Gd, Dy) superconductor, and CCT (Continuous-Cooling-Transformation) along with the TTT (Time-Temperature-Transformation) diagrams are suggested according to the isothermal and continuous cooling heat-treatments. The peritectic temperature of the 123 phases decreased approximately 3$0^{circ}C$ when the ionic radius of the rare-earth elements was reduced. The optimum cooling rate where BC and Cu-free phases do not exist was 0.001$^{circ}C$/s. At this cooling late, the 123 phase grew with a c-axis Perpendicular to the surface and had a well-distributed 211 phase. When the oxygen partial pressure was reduced Outing isothermal heat-treatment, the formation temperature of the 211 phase decreased. In addition, the formation temperature of the 123 phases decreased from 100$0^{circ}C$ (Nd-123) to 9$25^{circ}C$ (Gd-123), and finally 875$^{circ}C$ (Dy-123) according to the decrease in the ionic radius of the tare-earth elements. Compared to Nd-123, Gd- and Dy-123 had a better texture with a well-distributed 211 phase.e.