A sliding mode controller is proposed for the attitude control of spacecraft reorientation with attitude constraints. By introducing a potential function, a novel sliding function is designed. With the structure of the proposed sliding function, uniqueness of the equilibrium and fixed-time convergence are rigorously proven. Another advantage of the proposed controller is that the feasibility of attitude constraints can be proven not only on the sliding surface but also outside it. Moreover, the singularity issue of the proposed controller is resolved. Effectiveness of the proposed method is demonstrated by carrying out two numerical simulation.