This paper investigates the robust stability for systems with time-varying delay. An improved linear matrix inequality (LMI) based robust delay-dependent stability test is introduced to ensure a larger upper bound for time-varying delays affecting the state vector of an uncertain continuous-time system with norm-bounded type uncertainties. We construct a new class of Lyapunov-Krasovskii functionals combined with the descriptor model transformation to derive some delay-dependent stability criteria. The proposed method gives sufficient conditions for the robust stability of the system with time-varying delay under norm-bounded uncertainty. Numerical examples indicate that the proposed stability criteria effectively improves the existing results.