With the application of more and more new technologies, such as cloud computing, IoT, and big data, the available intelligent service scenarios become complex. For better service identification and recommendation, conversational AI bots need to construct user needs expression models accurately. Most traditional user needs expression models could do better in individual tasks but nearly not support the social requirements. To solve the challenge before, this study expands the Intention Tree Model for Personal Needs(ITM-PN) to the Intention Tree Model for Social Needs based on Negotiation(ITM-SN) to model different users' needs during the process of multi-user negotiation(initial, processing, ending). And finally, this study conducted a case study to prove the ITM-SN is thoroughly and effectively, which could be widely applicable in many fields.