This paper studies the problem of stability for continuous-time systems with differentiable time-varying delays. By using the information of delay derivative, improved asymptotic stability conditions for time-delay systems are presented. Unlike the previous methods, the upper bound of the delay derivative is taken into consideration even if this upper bound is larger than or equal to 1. It is proved that the obtained results are less conservative than the existing ones. Meanwhile, the computational complexity of the presented stability criteria is reduced greatly since fewer decision variables are involved. Numerical examples are given to illustrate the effectiveness and less conservatism of the obtained stability conditions.