Frequency‐selective surface (FSS) antennas are critical in modern communication systems, where optimizing their design for enhanced performance is essential. However, traditional methods often struggle with the complexity of FSS structures, leading to suboptimal designs. This paper addresses these limitations by proposing a novel CNN‐GNN hybrid network (CGHN) framework for FSS antenna optimization. The proposed methodology integrates convolutional neural networks (CNNs) for efficient feature extraction of spatial patterns within FSS designs and graph neural networks (GNNs) to model the relational dependencies between unit cells. This approach ensures that both local features and global interactions are captured, leading to more accurate and optimized antenna designs. The objective is to enhance the performance of FSS antennas by leveraging the complementary strengths of CNNs and GNNs, with an emphasis on improving design accuracy and efficiency. The novelty lies in the combination of CNN's localized pattern recognition with GNN's relational learning, which together enable a comprehensive understanding of the antenna's behavior. The proposed CGHN framework achieves a 96.78% accuracy rate in predicting optimal FSS designs, with a 23.84% boost in performance due to CNN‐driven feature extraction. Additionally, implementing stochastic gradient descent with gradient clipping increased the F1 score by 15%. Compared with existing techniques, the proposed method demonstrates significant improvements in both accuracy and efficiency, making it a superior choice for FSS antenna design optimization.