In this paper a leader-following consensus problem of second-order multi-agent systems with fixed and switching topologies as well as non-uniform time-varying delays is considered For the case of fixed topology a necessary and sufficient condition is obtained For the case of switching topology a sufficient condition is obtained under the assumption that the total period over which the leader is globally reachable is sufficiently large We not only prove that a consensus is reachable asymptotically but also give an estimation of the convergence rate An example with simulation is presented to illustrate the theoretical results (C) 2010 Elsevier Ltd All rights reserved