This paper concerns delay-dependent guaranteed cost control (GCC) problem for a class of linear state-delayed systems with norm-bounded time-varying parametric uncertainties. By incorporating the free weighing matrix approach developed recently, new delay-dependent conditions for the existence of the guaranteed cost controller are presented in terms of matrix inequalities for both nominal state-delayed systems and uncertain state-delayed systems. An algorithm involving convex optimization is proposed to design a controller achieving a suboptimal guaranteed cost such that the system can be stabilized for all admissible uncertainties. Through numerical examples, it is shown that the proposed method can yield less guaranteed cost than the existing delay-dependent methods.