When flexible spacecraft operates， disturbances such as the swaying of liquid fuel and gravity gradients cause the spacecraft system to exhibit strong nonlinearity and coupling characteristics. Thus， controlling its attitude deflection has always been a challenging problem. To solve this issue， this paper designs a H_∞ state feedback controller. The integrated disturbance term in the dynamic model of the flexible spacecraft is redefined， and combined with the kinematic model， the mathematical expression of the flexible spacecraft is formulated. The mathematical model of the flexible spacecraft is transformed into an H_{\mathrm{\infty }} state feedback control mathematical model. The theoretical applicability of the controller is demonstrated by mathematical theory. The mathematical model of the flexible spacecraft under H_{\mathrm{\infty }} state feedback control is simulated by simulation software. The results show that the designed H_{\mathrm{\infty }} state feedback controller can effectively achieve attitude stabilization and vibration suppression of flexible spacecraft， showing practical value.