Extracting meaningful features from sequences and devising effective similarity measures are vital for sequence data mining tasks, particularly sequence classification. While neural network models are commonly used to automatically learn sequence features, they are limited to capturing adjacent structural connection information and ignoring global, higher-order information between the sequences. To address these challenges, we propose a novel Hypergraph Attention Network model, namely Seq-HyGAN for sequence classification problems. To capture the complex structural similarity between sequence data, we create a novel hypergraph model by defining higher-order relations between subsequences extracted from sequences. Subsequently, we introduce a Sequence Hypergraph Attention Network that learns sequence features by considering the significance of subsequences and sequences to one another. Through extensive experiments, we demonstrate the effectiveness of our proposed Seq-HyGAN model in accurately classifying sequence data, outperforming several state-of-the-art methods by a significant margin.