The invention relates to a process for producing a tertiary amine, which includes reacting an alcohol with a primary or secondary amine gas in the presence of a catalyst with an agitating vessel under the stirring conditions where the ratio (Pg/P0) of agitating power at the time of the maximum flow rate of an introducing gas (Pg [W]) to agitating power at the time of no introduction of the gas (P0 [W]) becomes 10<-1.8Na >or more wherein Na is the gas flow number, and Na=Qg/nd<3 >whereupon Qg [m<3>/s] is the flow rate of an introducing gas, n [1/s] is the number of revolutions, and d [m] is the diameter of an agitating impeller.