Abstract: Fast terminal sliding mode control strategy is proposed for time-delay linear system with unmatched time-varying uncertainties.The terminal sliding mode uses nonlinear sliding surface to ensure the system reach the equilibrium point in finite time.When the extended sliding coefficient matching condition is satisfied,terminal sliding mode controller can have the system on the sliding surface be invariant to the unmatched time-varying uncertainties and time-delay elements.It also guarantees the reaching mode of the sliding surface and the stability of the close-loop system.Simulation results are used to illustrate the effectiveness of the presented terminal sliding mode control strategy.