This paper presents an H_∞ controller design method for a class of Networked Control Systems (NCSs) with bounded packet dropouts. The state feedback closed-loop NCS is modeled as a Markov system. A sufficient condition for stochastic stability with an H_∞ disturbance attenuation level is derived through a Lyapunov function, which is dependent on the upper bound of the number of consecutive packet dropouts. The corresponding state feedback control law is presented in terms of linear matrix inequalities (LMIs). A numerical example is finally provided to show the effectiveness of the proposed method.