This paper discusses the optimal tracking control of linear discrete time delay systems and its application to an industrial electric heater with pure delays. The system with control time delay and a direct path between input and output variables is discussed first, and then a general form of time delay systems is analysed. An extended state vector involving all time delay variables of the original system is constructed to obtain an extended new system without time delays. Using the optimal feedback control theory of LQI, the paper gives an optimal control tracking algorithm and the conditions for stability and exact tracking of closed-loop systems. Finally, a simulation study on an industrial electric heater is carried out. The result shows that, in the case of temperature setpoint changes, the optimal tracking control can result in fast exact tracking with small deviation.