A method of recovering cobalt and nickel includes the steps of: adding alkaline to an acidic solution containing aluminum together with cobalt and nickel, adjusting pH of the acidic solution to 5 to 7, and converting the cobalt, the nickel and the aluminum into hydroxides thereof; recovering the hydroxides by solid-liquid separation, mixing the recovered hydroxides with an alkaline solution, and leaching aluminum contained in the hydroxides under a liquid condition of pH 8 or more; and recovering a cobalt hydroxide and a nickel hydroxide that aluminum is separated therefrom by solid-separation on a leachate.