Zero-shot Relational Learning (ZRL) aims to perform knowledge graph completion when dealing with newly emerging relations without instances of them. However, existing ZRL methods typically depend on external knowledge beyond Knowledge Graphs (KGs), resulting in increased annotation costs and limited practical applicability. To address this issue, we propose a new **S**tructure-**A**ware paradigm for **ZRL**, termed **SAZRL**, that performs ZRL without relying on external knowledge. SAZRL leverages intrinsic structural patterns in KGs to bridge semantic correlations for new relations with existing ones. It constructs structure-aware conditional query graphs based on shared entities and adaptive relation updating module to generate representations for new relations based on the query graphs. We conduct extensive experiments on three real-world benchmarks, **NELL-ZS**, **Wiki-ZS** and **FB15K-ZS**, demonstrating that SAZRL consistently surpasses state-of-the-art ZRL methods, achieving up to **10.66%** improvement in **MRR** while reducing annotation costs and enhancing practical applicability. **The code and data are provided in supplementary materials.**