There has been a significantly increased amount of literature on various aspects of artificial intelligence (AI), but research on AI governance has been a considerably underdeveloped area. This study proposes a comprehensive framework for designing AI governance in the public sector to overcome the limitations of previous studies that primarily dealt with the fragmentary aspect of AI. Also, we applied the developed framework to the case of Korea by combining it with the rank-order survey questions that target experts. This case study presents how to use the framework and provides insight for other countries.