School climate has been reported to have an important impact on children’s achievement motivation, but the mechanism for the impact of school climate on left-behind children has not been fully explored. The purpose of this study is to investigate the roles of left-behind children’s learning adaptability and teacher support in mediating and moderating the relationship between school climate and achievement motivation. In this study, 1,417 left-behind children were surveyed. The results showed that: (1) after controlling for gender and age, the school climate still had a positive effect on the achievement motivation of left-behind children (c′ = 0.177, p < 0.001). (2) School climate perceived by left-behind children directly predicted their achievement motivation, and indirectly through their learning adaptability (a1 = 0.338, p < 0.001; b = 0.341, p < 0.001). In other words, left-behind children’s learning adaptability may play an intermediary role between school climate and achievement motivation. (3) The indirect effect of school climate on achievement motivation through learning adaptability was moderated by teacher support (a2 = 0.153, p < 0.001), and this indirect effect was more significant for left-behind children who perceived high teacher support. The research reveals the importance of school climate and teacher support to the growth and development of left-behind children, thus holding theoretical significance for improving the achievement motivation of left-behind children.