In this technical note, the weak convergence of a nonlinear high-gain tracking differentiator based on finite-time stable system is presented under some easy checkable conditions. An example is constructed by using homogeneity. Numerical simulation shows that this tracking differentiator takes advantages over the existing ones. This result relaxes the strict conditions required in existing literature that the Lyapunov function satisfies the global Lipschitz condition and the setting-time function is continuous at zero, both of them seem very restrictive in applications.