A distributed anti-disturbance control algorithm is proposed for spacecraft formation under undirected graphs, which does not require the transmission of velocity information or control acceleration, and ensures predefined-time synchronization. Under the effect of this controller, the three-axis components of all spacecraft states can simultaneously reach the target position, and the convergence time is unaffected by the spacecraft’s initial state. To achieve this objective, a novel sliding surface is designed that utilizes only the spacecraft’s own velocity information and formation errors. When the system state reaches the sliding surface and stays on there, it guarantees simultaneous convergence of all spacecraft formation errors. Furthermore, to guarantee that all components of the sliding surface achieve the predefined-time-synchronized stability, a new predefined-time-synchronized controller is introduced. Additionally, an effective disturbance observer is designed to compensate for external disturbances. Finally, through a numerical simulation, the effectiveness of the proposed algorithm is confirmed.