A novel switching-differentiator (SD) that can asymptotically track the time derivative of time-varying signal was previously proposed. This paper extends the previous SD to estimation of higher-order time derivatives. This study shows that higher-order time-derivatives can be estimated by connecting multiple SDs in cascade form. By successive applying the generalized Barbalat’s lemma, all higher-order tracking errors also approach zeros asymptotically. To illustrate the performance of the proposed higher-order switching differentiator, simulations were performed for estimating higher-order time-derivatives of a signal.