This paper is concerned with the control of the dual-spin turn (DST) of a spacecraft to regulate the spacecraft attitude. The DST is a method for attitude stabilization of a rotating spacecraft by transferring the angular momentum of the spacecraft to a single wheel. The proposed control law consists of feedforward (FF) and feedback (FB) control phases. The FF control is designed by optimizing the driving pattern of the wheel using the Differential Evolution (DE). In the FB control, the rate damping control and the attitude control around the wheel rotation axis are proposed based on the linearized error system around the stationary state of the spacecraft. By using the proposed control law, the DST is controlled step by step, and the spacecraft eventually becomes stationary at an arbitrary angle around the wheel rotation axis. The validity of the proposed method is verified by numerical simulations.