This paper is concerned with the attitude cooperative control of multi-spacecraft. With communication delays considered, a cooperative control strategy on SO(3) is proposed. The attitude of the spacecraft is described by the SO(3) method, and the control system is modeled with the communication topology. Based on this, the cooperative commands are designed in the form of rotation matrices. The relative errors on SO(3) are proposed to construct the cooperative controller, and the compensation filter is introduced to handle the time delay in the control system. Then, the stability analysis with the controllers on SO(3) is presented, and it guarantees the tracking of the commands so that the spacecraft could achieve attitude synchronization. The proposed method is verified by simulation, and the results demonstrate that the cooperative control method on SO(3) is effective.