This paper investigates cooperative tracking problems for multiple non-linear dynamic systems. The desired trajectory is only available to a portion of the agents. Treating the desired trajectory as a virtual agent, a terminal sliding mode (TSM)-based distributed control algorithm is designed only using the neighbours’ information. A decentralized observer is provided firstly to estimate the unknown external disturbances. Then, the Gaussian functions are introduced to approximate the second-order derivative of the inaccessible states. On this basis, we further develop a TSM-based cooperative tracking control algorithm for the non-linear dynamic systems such that the tracking errors of each agent converge to an adjustable neighbourhood of the origin in finite time. Finally, a simulation example is presented to illustrate the feasibility and effectiveness of the proposed approaches.