YBa2Cu3O7-x(=YBCO) single crystals were grown by flux method and the growing process of crystals was investigated. YBCO and 3BaO-7CuO composition powders were mixed by the ratio of 25 : 75(wt%), and the mixtures were melted at 105$0^{circ}C$ in a electric furnace with no temperature-gradient. Then the melt was cooled at a rate 2-1$0^{circ}C$/h in the above furnace. YBCO single crystal plate with average size of $1.5 imes$2.0$ imes$0.1㎣ were obtained in the cavities between crucible and solidified ingot, and the single crystals were oriented to <001> direction. The ingots of flux parts were analyzed by XRD and EDS for the purpose of presuming the growing process of the crystals. It was assumed that the divorced eutectic reaction, by which YBCO crystals were grown first and then BaCuO2 and CuO crystals, occured in the case of cooling rate faster than 2$^{circ}C$/h. When the cooling rate was 2$^{circ}C$/h, it was assumed that quasi-equilibrium eutectic reaction occured, so that YBCO, BaCuO2 and CuO crystals were grown at the same time.