This paper focuses on the problem of global practical output tracking for a class of high-order non-linear systems with time-varying delays (via state feedback). Under mild growth conditions on the system nonlinearities involving time-varying delays, we construct a state feedback controller with an adjustable scaling gain. With the aid of a Lyapunov-Krasovskii functional, the scaling gain is adjusted to dominate the time-delay nonlinearities bounded by the growth conditions and make the tracking error arbitrarily small while all the states of the closed-loop system remain to be bounded. Finally, a simulation example is given to illustrate the effectiveness of the tracking controller.