This article considers the problem of finite-time consensus for nonlinear multiagent systems (MASs), where the nonlinear dynamics are completely unknown and the output saturation exists. First, the mapping relationship between the output of each agent at the terminal time and the control input is established along the iteration domain. By using the terminal iterative learning control method, two novel distributed data-driven consensus protocols are proposed depending on the input and output saturated data of agents and its neighbors. Then, the convergence conditions independent of agents' dynamics are developed for the MASs with fixed communication topology. It is shown that the proposed data-driven protocol can guarantee the system to achieve two different finite-time consensus objectives. Meanwhile, the design is also extended to the case of switching topologies. Finally, the effectiveness of the data-driven protocol is validated by a simulation example.