This paper deals with the stability analysis and the stabilization for the class of continuous-time systems with time-varying delay. The time delay is assumed to be differentiable with respect to time with finite bound not necessary less one and appear in the state. Delay-dependent sufficient conditions on stability and stabilizability are developed. These conditions use some weighting matrices to reduce the conservatism. A design algorithm for a state feedback controller which guarantees that the closed-loop dynamics will be stable is proposed in terms of the solutions to linear matrix inequalities.