Abstract: Powdery alumina hydrate is produced from an alkylaluminum compound by hydrolysis of the alkylaluminum compound by water through the following steps; converting the alkylaluminum compound to an ether complex compound: partially hydrolyzing the ether complex compound in the presence of an non-reactive solvent at a temperature of not higher than about 150.degree.C with stirring so that no alumina hydrate is precipitated until at least 0.8 moles of water reacts with one mole of the alkylaluminum compound, thereby forming polyaluminoxane; completely hydrolyzing the resulting polyaluminoxane at a concentration of not more than about 3.0 grams-atoms as aluminum per liter of non-reactive solvent at a temperature of about 10.degree. to about 150.degree.C with stirring, so that one mole of the feed alkylaluminum compound may be ultimately hydrolyzed completely with 2 to 10 moles of water, thereby precipitating alumina hydrate; and then separating the resulting alumina hydrate from the non-reactive solvent.