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In this paper, the weighted average prediction (WAP) is introduced into the existing consensus protocol for simultaneously improving the robustness to communication delay and the convergence speed of achieving the consensus. The frequency-domain analysis and algebra graph theory are employed to derive the necessary and sufficient condition guaranteeing the second-order delayed multi-agent systems applying the WAP-based consensus protocol to achieve the stationary consensus. It is proved that introducing the WAP with the proper length into the existing consensus protocol can improve the robustness against communication delay. Also, we prove that for two kinds of second-order delayed multi-agent systems: 1) the IR-ones with communication delay approaching zero and 2) the ones with communication delay approaching the maximum delay, introducing the WAP with the proper length into the existing consensus protocol can accelerate the convergence speed of achieving the stationary consensus.