Within the development of brain-computer interface (BCI) systems, it is crucial to consider the impact of brain network dynamics and neural signal transmission mechanisms on electroencephalogram-based motor imagery (MI-EEG) tasks. However, conventional deep learning (DL) methods cannot reflect the topological relationship among electrodes, thereby hindering the effective decoding of brain activity. Inspired by the concept of brain neuronal forward-forward (F-F) mechanism, a novel DL framework based on Graph Neural Network combined forward-forward mechanism (F-FGCN) is presented. F-FGCN framework aims to enhance EEG signal decoding performance by applying functional topological relationships and signal propagation mechanism. The fusion process involves converting the multi-channel EEG into a sequence of signals and constructing a network grounded on the Pearson correlation coeffcient, effectively representing the associations between channels. Our model initially pre-trains the Graph Convolutional Network (GCN), and fine-tunes the output layer to obtain the feature vector. Moreover, the F-F model is used for advanced feature extraction and classification. Achievement of F-FGCN is assessed on the PhysioNet dataset for a four-class categorization, compared with various classical and state-of-the-art models. The learned features of the F-FGCN substantially amplify the performance of downstream classifiers, achieving the highest accuracy of 96.11% and 82.37% at the subject and group levels, respectively. Experimental results affirm the potency of FFGCN in enhancing EEG decoding performance, thus paving the way for BCI applications.