Based on the bidding mechanism, an autonomous mission planning method was proposed to solve the rapid response problem of unexpected tasks in the background of multi-satellite cooperative remote sensing, which considers the limited computing resources and the weak computing power on the satellite. In order to find an optimization algorithm that satisfies the requirements of on-board autonomous mission planning and enhances the rapid response capability of the constellation of the remote sensing satellites in unexpected situations, the multi-satellite collaborative planning modeling, algorithm design, and simulation analysis were studied. First, the mathematical model of autonomous mission planning on the satellite for multi-satellite autonomous collaborative task planning was constructed. Then, in the problem solving process, a complete task planning was reasonably decomposed into three processes including invitation for bid, bidding, and evaluation. With the solving process and the corresponding constraint inspection rules designed, the multi-satellite autonomous collaborative mission planning algorithm based on bidding mechanism was obtained. Compared with commonly used intelligent optimization methods, this method can significantly reduce the computational complexity and adapt to the tight computational resource constraints on the satellite. The simulation example shows that for a typical unexpected task, the average simulation running time of the algorithm was about 1 s, the response to unexpected tasks could be completed within 40 s, and the completion rate of the original planning task was fully guaranteed, which verifies the validity and the correctness of the method.