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In this paper, the attitude control algorithm of flexible spacecraft with unknown measurement delay and input delay based on disturbance observer is designed. The influence of measurement delay and input delay on the attitude control system and disturbance observer is analyzed. The disturbance estimation error equation is transformed into a differential system with a pure delay. Then, the observer gain is chosen based on the 3/2 stability theorem to ensure the stability and disturbance attenuation performance of the pure delay system. Next, the controller gain is designed based on the Linear Matrix Inequality (LMI) approach to guarantee the stability of the composite system and achieve H∞performance with two additive delays. The simulation results show that the proposed method can improve the anti-disturbance ability of the attitude control system.