Abstract: The well-posedness and stability of set optimization problems are discussed in the normed vector space. Firstly, The concepts for three kinds of well-posedness to set optimization problems and their relations are given. Secondly, under the local cone Lipschitz continuity the well-posedness of set optimization problems is characterized by using the analytical method. Finally, the Berge semi-continuity and compactness of minimal solution mappings are studied for parametric set optimization involving the cone Lipschitz continuous set-valued mapping.