In this paper, we first design a self-tuning distributed observer for second-order multi-agent systems which is capable of providing the estimation of the leader’s signal to various followers. We then further develop an adaptive sliding-mode controller to solve the cooperative tracking problem between leader and followers for second-order multi-agent systems subject to time-varying actuator faults and unknown external disturbances, which can ensure that the leader-following cooperative tracking errors converge to zero asymptotically. Finally, a simulation example is provided to demonstrate the effectiveness of the proposed controller. This control law offers three advantages: first, the problem of communication barriers among the leader and followers can be solved by the self-tuning distributed observer, which can calculate the observer gain online; second, a new type of adaptive sliding-mode controller is proposed by introducing a Nussbaum function; and lastly, the bounds of unknown actuator faults and unknown external disturbances can be adaptively estimated.