Motor imagery, as a paradigm of brain-computer interface, holds vast potential in the field of medical rehabilitation. Addressing the challenges posed by the non-stationarity and low signal-to-noise ratio of EEG signals, the effective extraction of features from motor imagery signals for accurate recognition stands as a key focus in motor imagery brain-computer interface technology. This paper proposes a motor imagery EEG signal classification model that combines functional brain networks with graph convolutional networks. First, functional brain networks are constructed using different brain functional connectivity metrics, and graph theory features are calculated to deeply analyze the characteristics of brain networks under different motor tasks. Then, the constructed functional brain networks are combined with graph convolutional networks for the classification and recognition of motor imagery tasks. The analysis based on brain functional connectivity reveals that the functional connectivity strength during the both fists task is significantly higher than that of other motor imagery tasks, and the functional connectivity strength during actual movement is generally superior to that of motor imagery tasks. In experiments conducted on the Physionet public dataset, the proposed model achieved a classification accuracy of 88.39% under multi-subject conditions, significantly outperforming traditional methods. Under single-subject conditions, the model effectively addressed the issue of individual variability, achieving an average classification accuracy of 99.31%. These results indicate that the proposed model not only exhibits excellent performance in the classification of motor imagery tasks but also provides new insights into the functional connectivity characteristics of different motor tasks and their corresponding brain regions.