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In the field of Brain-Computer Interface ( BCI) the recognition of natural hand movements through electroencephalography ( EEG) is crucial for achieving natural and precise human-machine interaction. However, attempts to enhance model generalization ability across different subjects using transfer learning are still rare in studies focusing on natural hand movement paradigms. Here, we investigate three natural hand movement paradigms of grasping, pinching and twisting through EEG experiments, and validate the effectiveness of two transfer learning algorithms , namely CA-MDM ( Covariance matrix centroid Alignment-Minimum Distance to Riemannian Mean) and CA-JDA ( Covariance matrix centroid Alignment-Joint Distribution Adaptation) on our experimental dataset. The results show that CA-JDA achieves average accuracies of 60. 51%+5. 78% and 34. 89% +4. 42% in binary and quadruple classification tasks, respectively, while CA-MDM performs 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.