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Spacecraft attitude hyper-agile maneuvering capability is a vital requirement for future space mission, such as space emergency rescue, etc. Traditional methods have the disadvantage of poor adaptability. Therefore, an attitude hyper-agile maneuvering controller for spacecraft with adaptive parameters is proposed to guarantee the performance without adjusting any parameters with uncertainties, including unknown inertia matrix, control torque saturation, angular rate saturation and changing desired attitude, etc. To satisfy the input constraint and guarantee the specific maximum angular velocity, a three-stage attitude scheduling method with adaptively tuned phases is defined. Then, a simplified backstepping control law is designed to track the prescribed attitude trajectory. Besides, considering the uncertainties, two adaptive parameters are implied based on the characteristics of the three-stage attitude maneuvering profile, to maximize the acceleration and to avoid the overshoot problem. Adaptive parameters are tuned automatically by heuristic observation. Simulation results illustrate the application of the proposed method for large angle maneuvering mission, and verify the effectiveness and advantages of the proposed controller with adaptive parameters.