Based on background radiation, material properties, orbit parameters, and the relative motion between LEO satellite body and solar panel, Davies-BRDF (bidirectional reflection distribution function) was used to establish the mathematical models of spectral and imaging characteristic of LEO satellite and calculate the satellite irradiance on entrance pupil and image plane of detector. Here, the surface of LEO satellite was divided into areas and each area was divided into grids. According to the orbit parameters of LEO satellite and detector, imaging condition of LEO satellite was analyzed and the judgment basis of imaging angle and scale was given. Taking different materials and shapes of satellites for example, these input parameters (the properties of structure, materials and orbit) were used to calculate the reflected radiation of every grid of satellite surface, and establish the mathematical models of reflection characteristic. The body coordinate of satellite was set and the relative positions of satellite, background radiation and detector were determined making use of coordinate conversion. In this paper, the imaging degrading effects were taken into consideration in the process of simulation. Simulated results of the satellite optical characteristic were decided by the relative position of the solar, the earth and the LEO satellite, as well as its geometrical shapes, flight figure and surface materials. The imaging results demonstrate that Davies-BRDF can simulate the reflection characteristics of the LEO satellite precisely and the simulated images was more accurate. © Springer Nature Switzerland AG 2018.