Abstract: To deal with the attitude control problem for rigid spacecraft, a method was proposed based on novel hyperbolic tangent reaching law and non-singular fixed time sliding mode surface. Firstly, for the spacecraft attitude control problem without disturbance, a novel fixed-time reaching law was designed based on hyperbolic tangent function, making the sliding mode variables converge to the origin in fixed-time by adjusting parameters only. Then, combined with the non-singular terminal sliding mode surface, a fixed time attitude controller was designed to make the spacecraft attitude converge to the origin in fixed-time for the attitude control problem without disturbance. Next, for attitude control problem in the presence of unknown disturbance, a two-layer adaptive finite-time sliding mode observer was designed to estimate external disturbances. And then, based on the output of the observer, a controller was designed with non-singular terminal sliding mode surface hyperbolic tangent reaching law to compensate the disturbances, and make the attitude converge to the origin in finite time. Finally, some numerical examples were illustrated to demonstrate the effectiveness of the proposed control scheme. Finally, numerical examples are illustrated to demonstrate the effectiveness the proposed control scheme.