The D-stability testing problem for continuous time-delay systems subjected to a class of highly structured parametric perturbations is addressed in this note. By means of the Lyapunov stability theorem, Razumikhin-type theorem, Gersgorin theorem, concept of spectral radius and norm and matrix measure techniques, we have developed several new sufficient conditions for guaranteeing that all characteristic roots of the above systems are located inside a specified disk D(alpha, r) with center at alpha plus j0 and radius r in the left-half complex plane. For the present results, it is not necessary to solve any Lyapunov equation which may be unsolvable though the Lyapunov stability theorem is utilized.