In this paper, we consider a multi-agent consensus problem with an accelerated motion leader and variable interconnection topology. To track such a leader, a neighbor-based local controller together with a neighbor-based state-estimation rule is proposed for each second-order follower-agent. The neighbor-based estimation rule is used to estimate the acceleration of the leader, which is assumed not to be measured by follower agents directly. By constructing a parameter-dependent common Lyapunov function, a sufficient condition is established to guarantee that each agent can follow the leader although the leader moves with an unknown time-variant acceleration. Moreover, the tracking error is estimated for the case that the unknown acceleration part of the leader has bounded derivative. Finally, a numerical example is given to illustrate the obtained result.