A new attitude controller is proposed for spacecraft whose actuator has variable input saturation limit. There are three identical flywheels orthogonally mounted on board. Each rotor is driven by a brushless DC motor (BLDCM). Models of spacecraft attitude dynamics and flywheel rotor driving motor electromechanics are discussed in detail. The controller design is similar to saturation limit linear assignment. An auxiliary parameter and a boundary coefficient are imported into the controller to guarantee system stability and improve control performance. A time-varying and state-dependent flywheel output torque saturation limit model is established. Stability of the closed-loop control system and asymptotic convergence of system states are proved via Lyapunov methods and LaSalle invariance principle. Boundedness of the auxiliary parameter ensures that the control objective can be achieved, while the boundary parameter’s value makes a balance between system control performance and flywheel utilization efficiency. Compared with existing controllers, the newly developed controller with variable torque saturation limit can bring smoother control and faster system response. Numerical simulations validate the effectiveness of the controller. A new attitude controller is proposed for spacecraft whose actuator has variable input saturation limit. There are three identical flywheels orthogonally mounted on board. Each rotor is driven by a brushless DC motor (BLDCM). Models of spacecraft attitude dynamics and flywheel rotor driving motor electromechanics The auxiliary design and a boundary coefficient are imported into the controller to guarantee system stability and improve control performance. A time-varying and state-dependent flywheel output torque saturation limit Stability of the closed-loop control system and asymptotic convergence of system states are proved via Lyapunov methods and LaSalle invariance principle. Boundedness of the auxiliary parameter ensures that the control objective can be achieved, while the boundary parameter’s value makes a balance between system control performance and flywheel Compared with existing controllers, the newly developed controller with variable torque saturation limit can bring smoother control and faster system response. Numerical simulations validate the effectiveness of the controller.