This research investigates the semi-global practical finite-time prescribed performance consensus control issue for a class of second-order multi-agent systems with unknown nonlinear functions. Unlike the previous finite-time control set by a finite-time performance function, we give finite-time control by constraining the terminal sliding manifold in a performance function. In addition, an adaptive neural network control scheme is designed, which simplifies the controller and avoids the chattering issue existing in traditional sliding mode control. Eventually, a novel adaptive finite-time prescribed performance consensus control strategy is designed, which ensures that all system variables are semi-globally practical finite-time stable and consensus errors of the multi-agent systems converge within the prescribed region in finite time. The effectiveness and practicality of the presented control strategy are evaluated by conducting simulation cases.