In this paper, we address the finite-time tracking consensus control problem for nonlinear multi-agent systems under no-cycle communication graph. Unlike most existing works of finite-time consensus, we focus on nonlinear multi-agent systems with lower triangular subsystems. Based on the local cooperative information among neighboring agents, we propose a tracking consensus protocol ensuring that all agents achieve consensus in a finite time. Finally, we give an example to illustrate the effectiveness of the proposed protocols.