In this paper, the problem of consensus for discrete-time networked multi-agent systems (NMASs) with a directed topology and diverse time-varying communication delays is investigated. By introducing the networked predictive control scheme, the predictions of states at current time, instead of available outdated states, are exploited to design a distributed consensus protocol, which compensates for communication delays actively. For NMASs with identical linear agents and bounded time-varying communication delays, necessary and sufficient conditions of the consensus are provided. Numerical simulations are given to compare the proposed networked predictive control method with the standard non-predictive way, and demonstrate the effectiveness of theoretical results. (C) 2015 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.