Abstract: In the framework of cooperative game with coalition structure, to investigate the axiomatization of coalition core along with the relationship of Owen value and coalition core, the definition of consistency and weak converse consistency is given by reduced game. The coalition core is characterized by means of individually rational, one-person rationality, consistency and weak converse consistency. The necessary and sufficient condition is given while solution is coalition core. The coalition core is unique on condition of the given reduced game and Owen value belongs to coalition core while the game is a strong convex game.