The present invention relates to a process for producing an aliphatic primary amine or an aliphatic secondary amine from an aliphatic alcohol with a high catalytic activity and a high selectivity. In the process for producing an aliphatic amine according to the present invention, a linear, branched, or cyclic aliphatic alcohol having 6 to 22 carbon atoms is contacted with ammonia and hydrogen in the presence of a catalyst formed by supporting a ruthenium component on at least one material selected from the group consisting of (B) a zirconia-containing composite oxide and (C) zirconia surface-treated with a metal by hydrolysis of (A) a ruthenium compound.