In this paper, we investigate the distributed adaptive leader-following consensus control for high-order nonlinear multi-agent systems with time-varying reference trajectory under directed topology subjected to mismatched unknown parameters and uncertain external disturbances. By introducing local estimators for the bounds of reference trajectory and a filter for each agent, a new backstepping based smooth distributed adaptive control protocol is proposed. It is shown that global uniform boundedness of all the closed-loop signals and asymptotically output consensus tracking can be achieved. Simulation results are provided to verify the effectiveness of our scheme. (C) 2017 Elsevier Ltd. All rights reserved.