We study in this paper the consensus problem for multi-agent systems with agents characterized by high-order linear systems with time delays in both the communication network and inputs. Provided that the open-loop dynamics of the agents is not exponentially unstable, but may be polynomially unstable, and the communication topology contains a directed spanning tree, a truncated predictor feedback approach is established to solve the consensus problem. It is shown that, if the delays are constant and exactly known, the consensus problems can be solved by both full state feedback and observer based output feedback protocols for arbitrarily large yet bounded delays. If it is further assumed that the open-loop dynamics of the agents only contains zero eigenvalues, the delays are allowed to be time-varying and unknown. Numerical examples are worked out to illustrate the effectiveness of the proposed approaches. (C) 2013 Elsevier Ltd. All rights reserved.