The problem of robust stabilization is considered for a class of uncertain linear time-varying systems with multiple time delays. In the paper, the upper bounds of uncertainties and external disturbances are assumed to be unknown. An adaptation law is introduced to estimate such unknown bounds, and by employing the updated values of these unknown bounds a class of memoryless state feedback controllers is proposed. Based on Lyapunov stability theory and Lyapunov-Krasovskii functional, it is shown that by making use of the proposed memoryless state feedback controller, the solutions of the resulting adaptive closed-loop time-delay system can be guaranteed to be uniformly bounded, and the states are uniformly asymptotically stable.