In this work, we propose one type of high-precision funnel control strategy to achieve attitude control for spacecraft control systems with external disturbances, based on which we program the whole control process such that the control error satisfies the design requirements. Firstly, we investigate the proposed funnel control strategy's transient performance. It is shown that if the initial value of the attitude tracking error is located in the funnel, which is designed based on the requirements of control precision, the tracking error can be guaranteed in this funnel at any time. Furthermore, considering the criteria for control value, we revise the design for the funnel function, ensuring the transient performance of the attitude control system. Finally, the proposed funnel control strategy and theoretic analysis are verified by numerical simulation, which shows the correctness and effectiveness.