Research on the use of software agents in P2P video streaming systems has recently emerged in order to meet the requirements such as time constraints, minimizing delay and efficient utilization of network resources. However parent selection and network awareness are not addressed properly in these leading studies. In order to fill this gap, we introduce the design and implementation of a Multi-agent System (MAS) for P2P video streaming in this paper. The construction of the MAS by applying a well-defined agent-oriented software engineering methodology is discussed. The internal structure of each agent in the proposed MAS is based on the well-known Belief-Desire-Intention (BDI) architecture. Experimental results show that the proposed MAS succeeds the related parent selection and promotes the system execution. BDI-based MAS design given in this paper can guide those researchers who aim to implement autonomous mesh-based P2P video streaming systems.