Lunar calibration is one of the important ways of satellite reflective solar bands on-orbit calibration. The most critical step in lunar calibration is to select the timing of observation. A rapid lunar observation forecast model is proposed, which is suitable for area-array cameras. The model first determines the distribution range of the time window by a fixed time step, and then selects several iso-distance scattering points on the projection circle of the moon in the direction of the satellite field of view, which is used to accurately determine the relationship between the moon and the satellite field of view. Subsequently, it uses the Fibonacci sequence search method to quickly calculate the time window of the moon entering and leaving the camera field of view. The simulation experiments show that the proposed model can improve the computational efficiency, reduce the computation cost, and make the prediction more accurate if compared with the conventional track propagation methods. The average deviation of visibility calculation accuracy between the proposed method and the Satellite Tool Kit (STK) method is in the sub-second scale.