Graph-level tasks such as classification and regression are critical in various domains, including citation network analysis, protein molecular analysis, and social network analysis, where understanding complex network structures is important. Although Graph Self-Supervised Learning (GSL) has proven effective for these tasks, it often falls short in capturing subtle yet crucial structural information. This paper presents GraphTEL, a novel Self-Supervised Graph Topology Embedding Learning framework designed to overcome the limitations of GSL by enhancing sensitivity to structural nuances through explicit learning of graph topological patterns. GraphTEL consists of dual topology learning, which explores both global and local topological characteristics, alongside well-designed pretext tasks optimized by topology-aware loss function. Experimental results and visualizations show that GraphTEL produces robust and discriminative graph-level embeddings, outperforming existing methods in graph-level tasks and offering a powerful tool for analyzing complex connectivity patterns across diverse applications. Significant improvements are observed in graph-level tasks. Our model outperforms the AD-GCL/JOAO by an average increase of 7.84%/7.25% and 0.098/0.122 on graph classification/regression tasks, respectively, demonstrating its advantages in comparison to the state-of-the-art models. The code is available at https://github.com/IntelliDAL/Graph/tree/main/GraphTEL .