This paper studies the secure consensus control of multi-agent systems where some agents are injected into malicious attacks and compromised. We focus on the distributed detection and identification of attacks on agents and the realization of consensus of agents against attacks. Firstly, we design monitors that can perform precise distributed attack detection. Then, we propose a distributed attack identification algorithm by constructing distributed observers. After that, a cooperative controller is proposed which ensures the normal control of systems by means of isolating the agents which are attacked. Finally, we validate our results through simulation examples.