A three-axis electro-optical tracking system can be used to track any space target in all azimuth.It can rapidly and accurately track the target in the alt-azimuth zenith blind region by rotating X axis.Several determinant methods to track the targets in the alt-azimuth zenith blind region by the three-axis electro-optical tracking system were introduced,such as target range determinant method,Z axis angular speed determinant method,preset blind region determinant method and so on.Determinant methods to track targets in the blind region at zenith have a directly effect on the tracking accuracy of the electro-optical tracking system with three-axis gimbal.Analysis and simulation results prove that the determination of the entry and exit points in the alt-azimuth zenith blind region with maximum angular velocity of Z axis could help three axes trackers to achieve better tracking accuracy and smooth transfer of tracking mode.