A raw material solution containing trivalent iron ions, or trivalent iron ions and ions of a metal element that partially substitutes Fe sites, and an alkaline aqueous solution for neutralizing the raw material solution are added to a reaction system to adjust the pH of the reaction system from 1.0 to 3.0 or lower. Hydroxycarboxylic acid is added to the obtained reaction solution and the pH of the reaction system is then neutralized from 7.0 to 10.0 or lower. The obtained precipitate of a substituent metal element-containing iron oxyhydroxide is coated with silicon oxide, followed by heating so as to form particles of ε-iron oxide in which Fe sites are partially substituted by other metal elements, and then, a slurry containing the particles is classified. The iron-based oxide magnetic powder has a particle shape close to a perfect sphere and is suitable for use in a magnetic recording medium.