The object of the present invention is to improve production efficiency of lithium hydroxide anhydride in a method for producing lithium hydroxide anhydride from lithium hydroxide hydrate by using a rotary kiln. The method for producing lithium hydroxide anhydride comprises steps of: supplying the lithium hydroxide hydrate to a region between a heating part which is the part of the furnace core tube surrounded by the heating furnace and one end of the furnace core tube; delivering the supplied lithium hydroxide hydrate toward the other end of the furnace core tube; feeding a drying gas with a temperature of 100° C. or higher to the region between the one end and the heating part of the furnace core tube, when the lithium hydroxide hydrate is supplied; and heating and dehydrating the lithium hydroxide hydrate by the heating furnace which is set to 230-450° C. during the lithium hydroxide delivering step, to form lithium hydroxide anhydride.