Abstract: To solve the problem that there are large errors and phase lags in the transition process arranged for the discrete input signals by the traditional tracking differentiator, an adaptive mesh tracking differentiator is proposed. According to the task requirements, the whole tracking process is divided into two parts: the rising and the stabilizing segments. The filtering factor and the rate factor are expanded into two-dimensional mesh, which is refined based on the preset mesh refinement strategy until the accuracy requirement is satisfied. The feasibility and effectiveness of the adaptive mesh based tracking differentiator are verified by several case studies. It can effectively deal with the great changing discrete input signals, and has the fast, accurate, and non-overshoot- tracking performance. Furthermore, there are no phase lags in both of the transition process and the extracted differential. In addition, when dealing with continuous signals, the proposed tracking differential also has these superior tracking effects. It is not affected by the size of the sampling step and has better adaptability.