According to the linear discrete system, a H_infinity controller with quantized measurements is designed in this thesis. By using Lyapunov function method fully, the sufficient condition of the controller that is obtained meet H_infinity performance index via linear matrix inequality (LMI) method. Compared with previous controller designing methods, this paper consider quantized measurements between the output of system and the observer. Finally, the toolbox of Matlab software and Simulation shows the validity of the proposed method by a numerical experiment.