The agent dynamics of most of the multi-agent systems in practice are second-order. However, there is no existing min-consensus protocol for such systems. In this paper, we deal with this problem by proposing the first second-order min-consensus protocol with provable convergence. It is not trivial to extend the min-consensus result for the first-order case to the second-order one. Under certain conditions, the proposed protocol can guarantee global asymptotic min-consensus, even for the case with jointly connected communication graphs. An illustrative example is presented to verify the theoretical results and the efficiency of the proposed protocol. (C) 2018 Elsevier Ltd. All rights reserved.