To investigate asteroid visibility in space-based optical surveillance using the radiative transfer theory， a brightness model of zodiacal and galactic light was introduced， and a signal-to-noise ratio （SNR） model for space-based asteroid surveillance was established. Combining the designed visible sensor with telescope performance parameters， the SNR and apparent magnitude of the target asteroid relative to the telescope over time were simulated. By considering the minimum SNR and solar avoidance angle， the maximum surveillance distance of a visible telescope deployed on an Earth-leading heliocentric orbit for asteroids of different diameters was calculated. The sensitivity of the SNR and apparent magnitude to the physical parameters of the asteroids was studied by changing the physical parameters of the asteroids. The results show that the distance of the asteroid relative to the telescope increased by approximately 0.09 AU， the apparent magnitude of the asteroid increased by approximately 0.51， and the SNR of the asteroid relative to a telescope with an aperture of 0.7 m decreased by approximately 3.78 during the period under observation. Owing to good coverage of the vicinity around the Earth with a radius of 0.05 AU， there is a unique advantage for visible telescopes deployed on Earth-leading heliocentric orbits to warn of asteroids approaching from the sunward direction； they can provide an early warning distance of 7.5 million km for asteroids with a diameter of 20 m. In the visible light band， the SNR and apparent magnitude of asteroids are sensitive to the visual albedo but not to the temperature and visual emissivity. The model established in this study provides a theoretical basis for the dynamic analysis of the SNR and the assessment of early warning distances for space-based optical surveillance of asteroids.