Summary This paper investigates the consensus problem for discrete‐time networked multiagent systems, where the information is exchanged through a shared network with communication delays. Based on the event‐triggered communication scheme together with the networked predictive control scheme, a novel distributed adaptive model‐based event‐triggered predictive control protocol is proposed to reduce the network communication burden and compensate for the communication delays actively. By using the virtual interval segmentation technique and the time‐delay modeling method together with defining a set of switching signals, the closed‐loop systems are established in forms of switching time‐delay systems. The problem of simultaneously deriving the controller gain matrix and the event‐triggering parameter matrices is cast into standard linear matrix inequalities problem. A convincing simulation example is given to demonstrate the theoretical results.