Crude fumed silica resulting from pyrogenic hydrolysis is purified by continuously feeding particulate silica and steam or a mixture of steam and air in a steam/air volume ratio of at least 1/2 through an upright column from its bottom toward its top for forming a fluidized bed within the column at a gas linear velocity of 1 to 10 cm/sec. and a temperature of 250.degree. to 400.degree. C., whereby steam deprives the particulate silica of the halide borne thereon, and removing fine particulate silica from which the halide has been eliminated from the top of the column. Using a simple apparatus, pure fine particulate silica is collected at a low cost of energy consumption.