Sustainable development research has grown in the past two decades, leading to key-competence-oriented teaching, which emphasises developing skills necessary for the 21st century. However, limited research focuses on the development of key competences into multilingual education. Through literature analysis on key competence, it is found that while existing frameworks highlight the importance of cyber competence, the Chinese 5Cs model does not include it as an explicit key competence. This study proposes a 6Cs key competence framework, adding Cyber competence to Cultural Competence, Critical Thinking, Creativity, Communication and Collaboration. Furthermore, a 6Cs key-competence-oriented curriculum design model is proposed. Based on this model, the study details the design of a 6Cs key-competence-oriented English curriculum, using the Korean ethnic group as an example. The curriculum is structured into three phases: (1) preparation that involves understanding learners' needs, creating authentic contexts, and designing relevant tasks; (2) teaching in which diverse and multicultural discourse materials are utilised to develop students' key competences; and (3) assessment that focuses on evaluating students' progress in acquiring the 6Cs competences. The study provides a reference for designing key-competence-oriented curricula to promote sustainability-oriented competences, particularly for ethnic students.