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.