On the platform of international cultural exchange, the traditional Chinese culture, with its rich content, shines brightly in the world. Tang poetry is an important part of traditional Chinese culture and is also loved by many foreign readers. Therefore, exploring effective translation strategies is one of the important tasks to promote the dissemination of Tang poetry. Untranslatability exists in the translation of Tang poetry, which is one of the key problems troubling translators. In the existing research, there is still a gap in how to solve the untranslatability of Tang poetry, and there is a lack of effective and systematic translation strategies. The theory of Three Beauties is an important translation theory put forward by Xu Yuanchong, a leading scholar in Chinese translation circles. The theory of Three beauties requires that the translation should conform to three standards: beauty of sound, beauty of form, and beauty of meaning. This paper chooses the case analysis method and analyzes some cases of Xu Yuanchong's English Translation of 300 Tang Poems based on the theory of three beauties to explore how to deal with the untranslatability of Tang poems in line with the standard of three beauties. This paper divides the case into two parts: language and culture. Author comes up with translation strategies to deal with these two types of untranslatability. This paper focuses on the compensatory strategies of Tang Poems found by the author when reading Xu Yuanchong's English Translation of 300 Tang Poems. This strategy is an innovation of the previous compensation methods, and it also shows the translator's overall understanding of the text for readers to read. According to the research findings, the author concludes that the most important thing for translators is to understand the connotation of Tang poetry and use translation strategies according to the specific situation.