Graphs play a crucial role in modeling relationships between entities across various applications. Workloads on graphs are typically categorized into transactional and analytical workloads. Many scenarios now require handling both types of workloads simultaneously. However, most existing graph storage systems are optimized for only one type of workload and cannot efficiently handle both simultaneously. In this study, a new graph storage system, HGraph, is proposed to address this issue. A data structure tailored for hybrid workloads is designed through careful analysis of the access patterns of both workload types. In addition, HGraph introduces a multi-version concurrency control (MVCC) implementation based on undo logs, which is memory-efficient and improves traversal performance. HGraph also adopts copy-on-write and optimistic concurrency control strategies to optimize transaction processing, further enhancing system concurrency. Extensive experiments on both real-world and synthetic datasets demonstrate that HGraph outperforms other graph storage systems.