Crystal growth of YBa2Cu3Ox superconductive oxides was investigated through the zone melting of Y123 fibers. The single faceted continuous structure was obtained at growth rates up to 3 mm/h. Although a similar interface structure was achieved at growth rates up to 6 mm/h, it consisted of several grains caused by nucleation and overgrowth. The compositional analysis revealed that the liquid composition near the growth interface of the sample was shifted to the CuO rich side, which might be caused by the enhanced compositional shift in the diffusion boundary layer. Due to this compositional shift during solidification, there would be a difference of supersaturation in the liquid for the growth of Y123 and a crystal nucleated in this region can overgrow the pre-existing crystal, which could cause the breakdown of the continuous growth of Y123 crystals.