The growth of Y1-zNdzBa2Cu3Ox single crystals has been carried out using self-flux Ba3Cu10O13 in alumina crucibles under a horizontal temperature gradient. The optimum growth conditions such as solute-to-flux ratio, maximum growth temperature, cooling rate, etc. were obtained by investigating the pseudo-binary Y0.5Nd0.5Ba2Cu3Ox-Ba3Cu10O13 phase diagram and crystallization mechanism of Y0.5Nd0.5Ba2Cu3Ox using in situ high-temperature optical microscopy. Plate-like Y1-zNdzBa2Cu3Ox crystals up to a size of 7.3 x 5.8 x 1.28 mm(3) exhibiting superconductivity at 93 K have been grown. The crystallinity of the grown crystals has been confirmed by Laue X-ray backscattering measurements.