A finite-time bounded tracking control problem is investigated for a class of linear continuous systems with time-delay. Firstly, by applying a derivation method in the theory of preview control to constructing the error system with time-delay, the error signal is included in the state vector of it and then considered as the output vector. Then, the problem is transformed into an input-output finite-time stability problem of the closed-loop system of the error system, by designing a memory state feedback controller for the error system. Forthermore, based on the research methods of input-output finite-time stability and linear matrix inequation methods, the controller gains formulated in forms of linear matrix inequalities are provided by constructing a Lyapunov-Krasovskii functional. From this, a finite-time bounded tracking controller of the original system is obtained. Finally, a numerical example is given to illustrate the effectiveness and superiority of the proposed controller.