In this study, the finite-time cooperative tracking issue for non-linear multi-agent systems with stochastic disturbances is addressed. Different from the existing asymptotical stable control, the finite-time cooperative control can ensure the outputs of agents reach agree in finite time by raising a novel finite-time stability criterion. The radial basis function neural networks are employed to cope with the unknown non-linearities caused by the non-linear non-strict feedback form. Moreover, this study designs a new adaptive quantised control strategy to reduce communication burden. With such a control scheme, the tracking errors converge to a small area of the origin in finite time. Finally, some numerical simulation results are presented to testify the effectiveness of the approach proposed in this study.