A novel approach to mixed H₂/H∞ control of spacecraft large angle attitude maneuvers is proposed based on sum of squares (SOS) optimization. By using modified Rodrigues parameters, the attitude dynamics of the spacecraft is represented in terms of linear parameter varying (LPV) systems. To reduce the designed conservativeness, a new mixed H₂/H∞ performance criterion is presented by introducing additional slack matrix variables, which eliminates the coupling terms between system matrices and Lyapunov matrix. Based on this, a sufficient condition for the existence of mixed H₂/H∞ controller is derived by using Lyapunov approach and SOS optimization. Finally, the H₂/H∞ controller design problem is converted into a parameter optimization problem with SOS constraints.