In this paper, attitude maneuver control without unwinding phenomenon is investigated for rigid spacecraft. First, a novel switching function is constructed by a hyperbolic sine function. It is shown that the spacecraft system possesses the unwinding-free performance when the system states are on the sliding surface. Based on the designed switching function, a sliding mode controller is developed to ensure the robustness of the attitude maneuver control system. Another essential feature of the presented attitude control law is that a dynamic parameter is introduced to guarantee the unwinding-free performance when the system states are outside the sliding surface. The simulation results demonstrate that the unwinding phenomenon is avoided during the attitude maneuver of a rigid spacecraft by adopting the constructed switching function and the proposed attitude control scheme.