The space-time distribution characteristics of clutter under the airborne bistatic radar system are heavily dependent on the configuration of bistatic radar. For the airborne bistatic radar system, to solve the problem that the radar configuration scene is in time-varying state due to the relative motion between the carriers, the fixed ground coordinate system was constructed. By using the coordinate transformation method, the analytical expression of bistatic range sum unit and the clutter echo expression were derived, and the mathematical model of clutter in a time-invariant coordinate system was established. Then the space-time distribution characteristics of clutter under airborne bistatic radar system and the influence of bistatic radar configuration on clutter distribution were theoretically analyzed and simulated, which verified the validity of the clutter model. The simulation results show that clutter distribution is greatly different under four flight configurations, i.e., consistent heading, parallel heading, vertical heading, and intersecting heading. The smaller the bistatic range sum is, the more the angle-Doppler trace disperses, the faster the Doppler frequency changes with the range, and the stronger the range correlation is. However, with the increase of bistatic range sum, clutter angle-Doppler trace gradually approaches, and range dependence of clutter is relatively reduced. The radar clutter model with fixed coordinate system is independent of the transceiver platform, which avoids the repeated modeling caused by the platform movement and extends the range of clutter model, which lays a foundation for the study of clutter suppression for airborne bistatic radar.