Knowledge graph (KG), as a novel knowledge storage approach, has been widely used in various domains. In the service computing community, researchers tried to harness the enormous potential of KG to tackle domain-specific tasks. However, the lack of an openly available service domain KG limits the in-depth exploration of KGs in domain-specific applications. Building a service domain KG primarily faces two challenges: first, the diversity and complexity of service domain knowledge, and second, the dispersion of domain knowledge and the lack of annotated data. These challenges discouraged costly investment in large, high-quality domain-specific KGs by researchers. In this paper, we present the construction of a service domain KG called BEAR. We design a comprehensive service domain knowledge ontology to automatically generate the prompts for the Large Language Model (LLM) and employ LLM to implement a zero-shot method to extract high-quality knowledge. A series of experiments are conducted to demonstrate the feasibility of graph construction process and showcase the richness of content available from BEAR. Currently, BEAR includes 133, 906 nodes, 169, 159 relations, and about 424, 000 factual knowledge as attributes, which is available through github.com/HTXone/BEAR.