Tracking of command constant references is a tracking control problem of fundamental importance. This problem for linear time-varying delay systems in the presence of actuator failures is solved in this article. The linear time-varying delay system with actuator failures is modelled as a switched linear time-varying delay system by utilising switching systems theory and a suitable control scheme. The polytopic technique is employed in order to cope with the time-varying, delay-derivative term in case its absolute value might exceed one. On the grounds of the average dwell-time approach, a switching tracking control law that is immune to actuator failures is designed and the conditions are derived such that the output of the linear time-varying delay system tracks given constant command references. Two illustrative examples along with the respective numerical and simulation results are presented to demonstrate the effectiveness of the proposed method.