The Appraisal Theory intends to study how the stance, the opinion and the attitude of language users are realized in discourses. This paper discusses the attitudinal meanings of Judgement in the inaugural addresses by the US presidents during the Cold War under the framework laid down by Martin and White. It has been found that the attitudinal meanings of Judgement account for the most part of all the attitudinal meanings in all the 11 addresses, and that the positive Judgements are foregrounded by its high percentage in all the attitudinal meanings of Judgement. The features in the use of attitudinal meanings of Judgement serve the purpose of the presidential inaugural addresses very well, i.e. to convey a new administration’s commitment to their future work and to win support from the audience.