In the field of Brain-Computer Interfaces (BCI), the recognition of natural hand movements through EEG is crucial for achieving natural and precise human-machine interaction. However, attempts to enhance the generalization ability of models across different subjects using transfer learning are still rare in studies focusing on natural hand movement paradigms. Addressing this issue, this paper conducted EEG experiments with three natural hand movements: grasping, pinching, and twisting. We validated the effectiveness of two transfer learning algorithms, CA-MDM and CA-JDA, on the experimental dataset. The results showed that CA-JDA achieved average accuracies of 60.51%±5.78% and 34.89%±4.42% in binary and four-class tasks, respectively, while CA-MDM performed at 63.88%±4.59% and 35.71%±4.84% in the same tasks, highlighting the advantages of Riemannian space-based classifiers in handling covariance features. This study not only confirms the feasibility of transfer learning in natural hand movement paradigms but also aids in reducing calibration time for BCI systems and implementing natural human-machine interaction strategies.