爱国 is a separable verb (离合词) meaning 'to love one's country'. It consists of the verb 爱 and the object 国, so you can insert aspect markers, complements, or modifiers between them — for example, 爱了一辈子的国 ('loved one's country for a lifetime'). As a verb, it takes no direct object (you don't say 爱国中国); as an adjective, you can say 很爱国 ('very patriotic') or 爱国的人 ('a patriotic person').