An anti-off-target control method for small video satellite target tracking based on visual field zoning was proposed to address the problem of high initial relative angular velocity between small video satellite and observation targets, which can easily deviate from the camera field of view and cause off target. This method divided the rectangular imaging field of the satellite camera into inner and outer parts according to the inscribed circle. The inner and outer parts of the inscribed circle were designed with tracking controllers based on potential function and Euler rotation method respectively. By using the Barbarat‘s lemma, the asymptotic stability of control laws in two parts was proved, and it was also proved that the potential function controller can ensure that target would not leave the inscribed circle of visual field after entering it. Through controller comparison and simulation, the results show that the Euler rotation method has a stronger ability to suppress target deviation from the field of view compared with PD control. Compared with the full Euler rotation method, the field of view partition control combining the Euler rotation method and potential function method can effectively achieve anti-off-target control for faster maneuvering targets, thereby achieving continuous tracking and observation.