This paper discusses the practical finite-time consensus control problem for unknown nonlinear singular multi-agent systems. First, the double estimation problem in the systems is solved. The observer is employed to provide the estimate of the system state, and then the neural network technique is adopted to approximate the unknown nonlinearity, where the estimation of the unknown parameter is provided by the designed adaptive law. Furthermore, the fully distributed adaptive control protocol is developed in the leader-following framework, and the protocol guarantees that the systems achieve practical consensus in finite time. Finally, an example is given to verify the effectiveness of the control scheme.