In this paper we consider finite-time consensus control for a group of second-order systems, including double-integrator systems and nonlinear mechanical systems. Distributed controllers are designed such that a consensus is reached while all the agents in the multi-agent system suffer from input saturation. Firstly, we propose distributed controllers for multiple double-integrator systems under the leader–follower scenario while only part of the agents have access to the leader. We also assume that the velocities of the agents are not measurable, thus an observer is designed for each of the agents. Secondly, the methodology is extended to the leader–follower consensus control for a group of nonlinear mechanical systems. It is shown that the states of the mechanical systems can reach a consensus within finite time under input saturation. Finally, simulation results illustrate and verify the effectiveness of the proposed schemes.