Bio-inspired Design (BID) is a method that draws principles from biological systems to solve complex real-world problems. While diverse knowledge-based tools have served BID, the retrieval and reasoning capabilities of knowledge graphs have not been explored in BID. This study introduces a novel knowledge graph-based BID approach, exploiting the power of knowledge graphs to support BID. In the approach, a comprehensive ontology is defined and then applied to construct a BID-specific knowledge graph, enabling efficient representation of the diverse and rich biological knowledge. The knowledge graph supports BID by facilitating knowledge retrieval and reasoning. Retrieval in BID is accomplished by finding potential links between biological systems and relevant design applications. Reasoning in BID is supported by a link prediction model that follows the design process of mapping from biological systems to design applications. Two case studies are conducted to demonstrate the effectiveness of the approach. The first case shows that our approach outperforms other benchmarks in retrieving related biological knowledge, and the second case presents how the link prediction model aids in generating relevant and inspirational design ideas.