H∞ stabilization problem for a class of linear systems with time-varying norm-bounded uncertainty is studied by means of hybrid state feedback strategy. Suppose that there exist finite candidate static state feedback controllers in a set of controllers, and none of the individual controller makes the systems stabilizable with H∞ disturbance attenuation. When the gain matrices of state feedback controllers are known, based on single Lyapunov function technique and convex combination condition, a switching law which makes the uncertain switched linear system stabilizable with H∞ disturbance attenuation is constructed. When the gain matrices of state feedback controllers are unknown, multiple Lyapunov function technique is employed to derive a sufficient condition for the uncertain switched linear systems to be stabilizable with H∞ disturbance attenuation. Moreover, the existence of two static state feedback control laws is given in terms of the solvability of two coupled linear matrix inequalities. Finally, a simuIation example illustrates the main results of this paper.