The current data-driven underwater object detection methods have significantly progressed. However, there are millions of marine creatures in the oceans, and collecting a corresponding database for each species for similar tasks (such as object detection)is expensive. Besides, marine environments are more complex than in-air cases. Water quality, illuminations, and seafloor topography may lead to domain shifting with visual instability features of underwater objects. To tackle these problems, we propose a few-shot adaptive object detection framework with a novel two-stage training approach and a lightweight feature correction module to accommodate both image-level and instance-level domain shifting on multiple datasets. Our method can be trained in a source domain and quickly adapt to an unfamiliar target domain with only a few labeled samples. Extensive experimental results have demonstrated the knowledge transfer capability of the proposed method in detecting two similar marine species. The code will be available at: https://github.com/roadhan/FSCW