This article presents the arguments for and against liberalism concerning the justice and differences of cultures or social groups. Contemporary liberalism has been criticized by many theorists on its insensitivity to differences between cultures and social groups. The topic concerning the demand for recognition by minority cultures and disadvantaged groups is one of the major concerns of both liberal and anti-liberal camps. According to anti-liberal theorists (mainly Marion Young in this article), the liberal conception of justice is inadequate in dealing with cultural minorities and marginalized groups. In order to accommodate non-liberal ways of life, some special rights attached to cultures or groups collectively should be recognized in addition to the equal rights accorded to each in dividual in a liberal state. To meet this challenge, many liberals (Joseph Raz, William Galston, and Will Kymlicka) try to argue that the so－called collective rights can be justified within a modified liberal theory of justice. Liberalism, therefore, can accommodate cultural minorities fully. Liberals` answer, however, does not satisfy Nancy Fraser. She tries to find a new way to solve the problem posed by the politics of recognition.