Steady-state visual evoked potential (SSVEP) is an essential signal type in brain-computer interface (BCI) systems, widely utilized in BCI research due to its high stability and ease of operation. While previous studies have achieved significant progress in SSVEP signal classification, challenges such as low signal-to-noise ratio, non-stationarity, and individual variability still persist. To further enhance the accuracy and practicality of SSVEP classification, this paper proposes a novel neural network architecture—Gam-EEGNet—that combines a global attention mechanism with EEGNet. EEGNet, known for its compact, efficient, and adaptive structure, plays a critical role in SSVEP signal processing. By incorporating a global attention mechanism into EEGNet, Gam-EEGNet can more accurately extract and represent SSVEP signal features, effectively reducing individual variability and noise interference. Experiments were conducted using SSVEP EEG data encompassing 12 different frequencies, and the performance of Gam-EEGNet was compared with that of other mainstream deep learning methods, including CCNN, FB-tCNN, and SSVEPNet. The results demonstrate that Gam-EEGNet outperforms these methods in terms of classification accuracy and information transfer rate (ITR) across different time windows, particularly achieving a classification accuracy of 86.58% within a short 0.7-second time window. In a 1-second time window, the average recognition accuracy across multiple subjects exceeded 95%, with an ITR above 189 bits/min. Moreover, Gam-EEGNet showed better convergence and stability during training, with faster convergence and lower training errors. These results indicate that Gam-EEGNet offers significant performance improvements in SSVEP signal classification, making it especially suitable for real-time BCI systems requiring rapid response, with broad application potential.