In recent years, unmanned aerial vehicles (UAVs) have had excellent performance in various fields, but their frequent component faults often lead to damages and serious accidents, so it is crucial to carry out timely fault diagnosis for them. Deep learning is widely used in the field of UAV fault diagnosis due to its superior feature extraction capability, but the increasing complexity of UAV faults and the scarcity of data have limited the development of deep learning in this field. To address the above problems, this paper proposed an Attention-based Joint Multi-Spatial Shared Knowledge Network (A-MSKN) for multi-objective fault diagnosis of UAVs under small samples. A-MSKN considers both complementary relationships between different tasks and intra-task dependencies within the same task for individual fault samples in different time intervals. Firstly, a single fault sample is divided into multiple sub-samples based on different time slices, and different sub-samples are coded to obtain different feature sub-spaces. Then, a sharing unit based on attention is designed to share not only the different feature subspaces within a task but also the features related between different tasks in a more fully shared way, to obtain more fault information for fault diagnosis under small samples. Finally, the effectiveness of the A-MSKN in the case of small samples was verified by testing it on real faulty flight data.