Abstract: The aim of this paper is to give an effective H_∞ control way and precise numerical method for a single-axis mechanical arm system in Hamilton system. The dynamic equation of a flexible mechanical arm with single-axis is established. The H_∞ control way of disturbance attenuation in control theory is used for the control problem. In the process of numerical simulation, the traditional differential methods are abandoned. Rather, the H_∞ control problem is computed with the help of established time precise integration algorithm in linear dynamic system, in which the state equation and Riccati equation are solved successfully. A numerical example is given, showing the effectiveness of the present method.