The weighted average prediction (WAP) is introduced into the existing consensus protocol to simultaneously improve the robustness to communication delay and the convergence speed of achieving the consensus. It is proved that for a supercritical-delay multi-agent system, introducing the WAP can improve not only the robustness against communication delay but also the convergence speed, provided that the length of the WAP is chosen properly. The implementation of the WAP-based consensus protocol is investigated and simulations are provided to demonstrate the effectiveness of the theoretical results.