This paper primarily focuses on the attitude tracking control issue of a rigid spacecraft and the fixed-time convergence problem of the closed-loop system states, due to the double-valued characteristic of the quaternion description method and the unwinding problem caused by it, a fixed-time anti-unwinding sliding mode attitude tracking control law is designed by using the sliding mode control method. Employing the sliding mode control technique, a fixed-time anti-unwinding sliding mode attitude tracking control law is devised. In conjunction with Lyapunov stability theory, the anti-unwinding characteristic of the closed-loop system and the convergence stability of the system states are demonstrated.