Graph representation learning aims to capture the structural and relational information in graphs. Recently, Euclidean space-based methods have achieved tremendous success. However, Euclidean space exhibits structural distortion problems when modeling graph data with tree structures or hierarchy, limiting the model’s performance. Based on this, researchers introduce Hyperbolic space to preserve the original structural information, but computations in Hyperbolic space rely on inverse trigonometric functions, resulting in increased computational complexity. How to learn in multi-spaces and make use of their advantages deserves careful consideration. This paper proposes a Hybrid Graph Representation Learning (HGRL) model that trains in the Hyperbolic and Euclidean spaces jointly. Euclidean space possesses the ability to learn regular geometric and has efficient computations, while Hyperbolic spaces are better suited for representing hieranrchical and non-linear relationships. Technically, we utilize the Euclidean contrast loss to minimize distances between similar samples, helping tight clusters in the traditional space. Simultaneously, the Hyperbolic hierarchy loss and Hyperbolic uniformity loss enable the model to comprehend intricate hierarchical relationships and ensure a uniform distribution of the data on the Poincaré Ball. Extensive experiments in node classification, clustering, and visualization tasks demonstrate the effectiveness of the HGRL mode in capturing hierarchy structures. We also employed ablation studies to validate the indispensability of each component.