In this paper, we propose a methodology for compensation of attacks on consensus networks. We assume that the network achieves its desired consensus value under a normal operational setting i.e. when the networked system is not under attack. We propose an adaptive based technique to ensure that the networked system maintains its desired behavior when the system inputs are under some false-date injection attacks. The proposed method adaptively estimates attack signals and compensates their effects. We demonstrate the good performance of our proposed compensation scheme through simulation studies that consider both constant and time-varying attack signals.