Summary: Optimal control theory is applied to find the optimal rotational maneuver strategy of a pitch bias momentum spacecraft. Time-optimal and fuel/time-optimal control laws are each investigated separately. Conventional time-optimal control theory is adopted taking into account the gyroscopic effect embedded in the bias momentum spacecraft. The modal decomposition technique is not applicable to gyroscopic systems due to the skew-symmetric system matrix. Therefore, the analysis is conducted with physical coordinates with extra effort in comparison with working with modal coordinates. It turns out that the symmetric torque profile, which is a necessary condition for the rest-to-rest maneuver of generic structural systems, does not apply to gyroscopic systems.