The medals of the 19th Asian Games and the 4th Asian Para Games carry profound cultural connotations, and play a crucial role in shaping and disseminating the national image. In this work, the design solicitation and the design connotation of the Hangzhou Asian Games and Asian Para Games medals were elucidated with the help of the logic "Taoism, Fa, Xue, Qi, Shi". The integrated context of the preliminary review, the re-review and the final design was explored, starting the fourfold logic narrative of the national identity carrying of the "Taoism to clarify the direction" Asian Games medals, the design idea core of "Fa to establish the foundation", the national image construction of "Qi to carry the Taoism", and the cultural value sharing of "Harmony and co-prosperity". The cultural narrative with the medal as an important carrier demonstrated the aesthetic concretization of the Hangzhou Asian Games and Asian Para Games medals, conveying the efficacy of national identity and oriental poetry. The logic structure of "Taoism, Fa, Xue, Qi, Shi" unlocks the cultural narrative code of Hangzhou Asian Games medals, transcending cultural differences to achieve value sharing, and fully and multi-level displaying the national image of China's openness and inclusiveness and cultural confidence, providing some experience for the design of medals for international large-scale sports events and the construction of China's national image.