In order to reveal the law of image rotation caused by reflective two-dimensional fast-steering mirror in the optical system, and provide a mathematical model for optical offsetting image rotation, a typical application of reflective two-dimensional fast-steering mirror is constructed. By using the mathematical analysis method of space vector rotating around the axis and the reflection imaging law of planar mirror, the reflection image vector model of typical application scene of reflective fast-steering mirror is established. According to the vector model of the reflected image, the mathematical model of image rotation in the observation plane is given. The mathematical model and physical causes of image rotation in two-dimensional fast-steering mirror scanning with single axis and double axis are analyzed, and the simulation results of image rotation angle are given. It lays a theoretical foundation and provides an accurate mathematical model for the optical offsetting image rotation of the optical system based on two-dimensional reflective fast-steering mirror.