This study concerns the admissible consensus problem for networked singular multi-agent systems with communication delays and agents described by general singular systems. Only the information of outputs is available through the network. An observer-based networked predictive control scheme (NPCS) is employed to compensate for the communication delays actively. Based on NPCS and dynamic compensator (dynamic output feedback), a novel protocol is proposed. Based on graph, algebra and singular system theory, the necessary and sufficient conditions are given to guarantee existence of the proposed protocol. The conditions depend on the topologies of singular multi-agent systems and the structure properties of each agent dynamics. Moreover, a consensus algorithm is provided to design the predictive protocol. A numerical example demonstrates the effectiveness of compensation for networked delays.