Considering the high penetration of distributed energy resources (DERs), extensive communication networks are deemed necessary to realize the coordinated control of DERs in microgrids (MGs). The reliance on communication networks introduces potential cyber security issues into MGs. However, such attacks are difficult to be detected when a global situational awareness is lacking in distributed systems. In this paper, we analyze the impacts of cyber-attacks on communication links, local controllers, and master controller, which would drive MGs away from optimal operating points. We propose a cyber-attack resilient distributed control strategy in which each participant can detect and isolate corrupted links and controllers in a timely and economic fashion. The proposed control strategy is effective against time-varying attack signals and successive attacks while retaining the MG operational merits. The proposed control strategy is examined for different types of attacks. In this case, we consider various operating conditions and apply the time-domain PSCAD/EMTDC to the simulation and analyses of two MG systems.