Consensus recovery is one of the most important topics of multi-agent systems subjected to failures, but there are few literatures considering this theme. In this article, two disastrous failures are introduced and corresponding recovery programs are proposed to investigate the consensus recovery of multi-agent systems. The failures of multi-agent systems mainly refer to the failures to the agents and links. The cut-agent and cut-link are presented to better understand the disastrous failures of multi-agent systems, and they are the most important components of multi-agent systems. When the cut-agent and cut-link are removed from the systems, the multi-agent systems will become disconnected, and the neighbour agents of cut-agent are used to recover the consensus of multi-agent systems in this article. For different failures, the different measures are taken to restore the connectivity of multi-agent systems, so as to recover the consensus of multi-agent systems. Under the proposed recovery strategies, the convergence speed of achieving consensus of the resulting networks is considered as the main target. Moreover, there is a trade-off between the convergence speed and robustness of the resulting networks.