A method of alkylating the side chain of alkyl-substituted aromatic hydrocarbons. The method comprises the steps of thermally treating an alumina by calcining in air and then degassing under vacuum to prepare an alumina carrier, loading an alkali metal on the alumina carrier by an impregnation method using the alkali metal dissolved in liquid ammonia, thermally treating the alkali metal loaded alumina carrier under vacuum to prepare a catalyst, then reacting an alkyl-substituted aromatic hydrocarbon with an aliphatic monoolefin, using the catalyst, under an atmosphere substantially free of oxygen, water and carbon dioxide gas to alkylate the side chain of the alkyl-substituted aromatic hydrocarbon.