Transparent and blue ZnO:Ga (GZO) single crystals have been grown by the traveling-solvent floating-zone technique using the solvent B2O3 + MoO3 + Nb2O5. The crystals were typically 9-14 mm in diameter and 46-120 mm in length. The largest one was Φ12 mm × 120 mm in size. All GZO crystals were grown along the <001> direction. The growth rate was 0.3-0.5 mm/h, which was far faster than 0.1 mm/day of that grown by the hydrothermal method. The crystalline quality has been characterized by single crystal X-ray diffraction and X-ray rocking curve measurements. Ga substituted on Zn-site and was saturated at about 0.5 wt % of Ga2O3 addition. The GZO crystal doped with 0.5 wt % Ga2O3 has the lowest electrical resistivity of 1.083 × 10-3ω·cm and the highest carrier concentration of 1.78 × 1020 cm-3.