Predicting the diffusion cascades is a critical task to understand information spread on social networks. Previous methods usually focus on the order or structure of the infected users in a single cascade, thus ignoring the global dependencies of users and cascades, limiting the performance of prediction. Current strategies to introduce social networks only learn the social homogeneity among users, which is not enough to describe their interaction preferences, let alone the dynamic changes. To address the above issues, we propose a novel information diffusion prediction model named Memory-enhanced Sequential Hypergraph Attention Networks (MS-HGAT). Specifically, to introduce the global dependencies of users, we not only take advantages of their friendships, but also consider their interactions at the cascade level. Furthermore, to dynamically capture user' preferences, we divide the diffusion hypergraph into several sub graphs based on timestamps, develop Hypergraph Attention Networks to learn the sequential hypergraphs, and connect them with gated fusion strategy. In addition, a memory-enhanced embedding lookup module is proposed to capture the learned user representations into the cascade-specific embedding space, thus highlighting the feature interaction within the cascade. The experimental results over four realistic datasets demonstrate that MS-HGAT significantly outperforms the state-of-the-art diffusion prediction models in both Hits@K and MAP@k metrics.