The well-known lifted cover inequality is widely employed in solving mixed integer programs. However, it is still an open question whether an arbitrary project lifted cover inequality can be computed in polynomial time for a given minimal cover (Gu, Nemhauser, and Savelsbergh, INFORMS J. Comput., 26: 117–123, 1999). In this talk, we show that this problem is NP-hard, thus giving a negative answer to the question.