In this study, a novel adaptive neural network (NN)-based leader-following consensus approach is proposed for a class of non-linear second-order multi-agent systems. For the existing NN consensus approaches, to obtain the desired approximation accuracy, the NN-based adaptive consensus algorithms require the number of NN nodes to must be large enough, and thus the online computation burden often are very heavy. However, the proposed adaptive consensus scheme can greatly reduce the online computation burden, because the adaptive adjusting parameters are designed in scalar form, which is the norm of the estimation of the optimal NN weight matrix. According to Lyapunov stability theory, the proposed approach can guarantee the leader-following consensus behaviour of non-linear second-order multi-agent systems to be obtained. Finally, a numerical simulation and a multi-manipulator simulation are carried out to further demonstrate the effectiveness of the proposed consensus approach. © 2015 The Institution of Engineering and Technology.