.alpha.-Alumina comprising .alpha.-alumina single crystal particles which are homogeneous containing no crystal seed inside the particles; have an octa- or higher polyhedral shape; have a D/H ratio of from 0.5 to 3.0, wherein D represents a maximum particle diameter parallel to a hexagonal lattice plane of a hexagonal close-packed lattice of the particles, and H represents a diameter perpendicular to the hexagonal lattice plane; have a number average particle diameter of more than 5 .mu.m and not more than 30 .mu.m; have a sodium content of less than 5 ppm in terms of Na.sub.2 O; and have an alumina purity of not less than 99.90% by weight. .alpha.-Alumina in a powder form composed of .alpha.-alumina single crystal particles having a high punity, a fine and uniform composition, a narrow particle size distribution, and an octa- or higher polyhedral shape which are not aggromerates. The .alpha.-alumina of the invention is useful as an abrasive, a raw material for sintered products, a raw material for a encapsulations, a raw material for ceramic filters, etc. and, owing to its high purity, particularly useful as a raw material for single crystals, e.g., yttrium aluminum garnet (YAG), sapphire, ruby, etc. and as a raw material for high purity sintered products.