This paper proposes optimization of the PD controller gains by minimizing H infinity norm for flexible spacecraft attitude control. Solving the problem is known to be difficult because it is described by a bilinear matrix inequality (BMI) that cannot be transformed into linear matrix inequalities (LMIs). In order to solve it within practical computation time, we revise the branch and bound algorithm and incorporate the quantization of the variable domains. The ETS-VI mathematical model is used to demonstrate its ability.