With the global spread, the English language has become a lingua franca and a component of basic education in many Asian countries, making Asia one of the regions in the world with the largest number of English speakers. However, due to the rich cultural diversities of Asian societies, using English as a lingua franca in Asia implies that speakers need to develop not only communicative competence but intercultural communicative competence, so as to ensure successful communication among people from different Asian societies. Given that successful intercultural communication requires the speakers' appreciation of their cultural diversities, while celebrating certain similarities, promoting learners' cross-cultural awareness has become one of the important objectives of English language teaching in Asia. In this paper, I will draw on some sample analyses of Asian folktales which have been translated into English to (i) identify and explore the features of narrative structures and contents which can be seen as transcultural and others which can be highlighted as culture-specific, and (ii) discuss how such comparative analyses of narrative structures and contents in Asian folktales can be used to promote the cross-cultural awareness of English language learners in Asia. Implications for the socio-cultural-based English language teaching are offered.