Abstract: The joint achievement intention represents the common task of agents to achieve collectively and is an important concept to specify and analyze the social behaviors in multi-agent system. The paper discusses the meaning and characteristics of joint achievement intention, analyzes the limitation and problems in existing work, defines the joint achievement intention with new and clear semantics based on the logic framework of multi-agent system, specifies and proves its important properties. The formal model can be used to effectively support the development of multi-agent system.