This paper is concerned with robust H∞ control with guaranteed α-stability for uncertain linear time-delay systems using a linear matrix inequality approach. The uncertainty described in this paper is in the so-called quadratic constraint form which takes some well-known uncertainty descriptions as special cases. Two specific problems are tackled in this paper, namely the robust H∞ control with guaranteed α-stability for uncertain linear time-delay systems with unknown constant delay using memoryless static state feedback and the robust H∞ control with guaranteed α-stability for uncertain linear time-delay systems with bounded varying rate time-varying delay using memoryless static state feedback. We show that legibility of some LMIs will guarantee the solvability of the corresponding problem.