This study addresses the problem of distributed consensus for discrete-time networked multi-agent systems (NMASs) with communication delays in the transmission network. Different from existing techniques, the networked predictive control scheme is introduced to compensate for communication delays actively and overcome the difficulties induced by the delays. A distributed consensus protocol based on the predictions of states at current time is designed. For discrete-time NMASs with a directed topology and non-uniform constant delays, necessary and sufficient conditions for the consensus are given. Numerical examples are presented to demonstrate the effectiveness of theoretical results.