An eigenaxis tracking control algorithm is presented to provide rapid attitude tracking and synchronized rotation for on-orbit-servicing spacecraft. Based on the relative motion error dynamic equation and the similar strategy applied in move-to-rest attitude maneuver, the algorithm imported a parameter, which was used to describe the deviation degree related to eigenaxis, as a feedback to ensure that whole tracking is an eigenaxis rotation. Finally, It carries out the simulation, which indicates that smooth maneuver process, high tracking error, short tracking path and nearly optimal time are achieved after the whole tracking.