The establishment of a reliable method for the growth of bulk In–Ga–Zn–O single crystals is important not only to investigate the fundamental and peculiar properties specific to this material but also for its development for novel functional devices. Large bulk single crystals of InGaZnO 4 have been successfully grown using an optical floating zone method under a flow of dry-air at high-pressure. The stoichiometric InGaZnO 4 single crystals were obtained at a gas pressure of 0.9 MPa using a feed rod with a Zn-rich composition, where the lattice constants are a = 3.2990(4) Å and c = 26.018(3) Å as the hexagonal expression for the rhombic system (space group R m, No. 166). The as-grown single crystals exhibit a blueish colour, but become transparent after annealing in oxygen. Upon post-annealing, the carrier density, the conductivity in the ab-plane and the mobility at room temperature changes in the range from ∼10 20 to ∼10 17 cm −3 , from ∼2000 to ∼1 S cm −1 , and from ∼100 to ∼10 cm 2 /(Vs), respectively. In addition, we found that the conductivity along the c-axis is much lower than that of the ab-plane in InGaZnO 4 single crystals, and that the anisotropy increases with decreasing carrier density.