In this paper, we focus on the design of a multi-scenario robust MCS switching strategy for 5G LEO satellite adaptive transmission system. Firstly, we analyze and model the large- and small-scaling fading of the LEO satellite channel based on 3GPP 38.811 to obtain all the SNR points for the given scenario. Secondly, we carefully designed the direct input and feedback input of the convolutional neural network (CNN), which facilitates to explore higher-dimensional search space and learn the scenario-related features. Simulation results demonstrate that the proposed method shows excellent performance in both single-scenario and multi-scenario conditions. Compared with the fixed threshold switching strategy (combined with high precision SNR estimation) whose performance is very close to the theoretical upper bound, the average throughput can still be promoted by 3.4% and the average outage probability can be reduced from 4.8% to 1.4%. Moreover, the designed switching strategy effectively incorporate the combination of multiple scenarios schemes in the adaptive transmission process without channel sensing technology, which greatly improves the robustness of the system.