According to the optical scattering theory and the orbital dynamics, mathematical model of equivalent magnitude of space object was established with Bidirectional Reflectance Distribution Function (BRDF) by region classification, grid division and vector coordinates transformation. Combining with the noise resources in space-based imaging detection of space object, mathematical model of Signal-to-Noise Ratio(SNR) was put forward. On the basis of the structure, material, background and orbit parameters of the object and the orbit and performance parameters of the detector, equivalent magnitude and SNR of the Space-Based Infrared System(SBIRS) were calculated. It shows there is about three magnitudes difference in equivalent magnitude during the observation time, which leads to the correlated variation of SNR. The simulation results illustrate the validity of modeling method. The dynamic analysis of SNR for space-based imaging detection of space object is achieved.