Video image stabilization technology is a crucial foundation for applications such as video image target identification, monitoring, and tracking. Satellite video covers a wide range of areas with complex and similar types of objects on the ground and diverse video types. However, currently, there is a lack of a general high-precision satellite video stabilization method (VSM) that can be applied to different land cover types and imaging modes. This paper proposes a high-precision VSM based on the ED-RANSAC, an error elimination operator constrained by Euclidean distance. Furthermore, a set of accuracy evaluation methods to ensure the reliability of video stabilization are sorted out. This paper conducted video stabilization experiments using optical video data from the Jilin-01 satellite and airborne SAR video data. Under the precision evaluation criteria proposed in this paper, the optical satellite video achieved inter-frame stabilization accuracy of better than 0.15 pixels in different test areas. The overall stabilization accuracy was better than 0.15 pixels. Similarly, the SAR video achieved inter-frame stabilization accuracy better than 0.3 pixels, and the overall stabilization accuracy was better than 0.3 pixels. These experimental results demonstrate the reliability and effectiveness of the proposed method for multi-modal satellite video stabilization.