Bio-inspired design (BID) is a design methodology that employs biological analogies for engineering design, encompassing problem-driven and solution-driven BID. Solution-driven BID starts with knowledge of a specific biological system for technical design. Despite the proven benefits of solution-driven BID, the gap between biological solutions and engineering problems hinders its effective application, with designers frequently encountering misaligned problem-solution pairs and facing multidisciplinary knowledge gaps in the analogical transfer process. Therefore, this research proposes a large language model (LLM)-based concept generation method, designed to automatically search for problems, transfer biological analogy, and generate solution-driven BID concepts in the form of natural language. A concept generator and two evaluators are identified and fine-tuned from the LLM. The method is evaluated by an ablation study, machine-based quantitative assessments, and human subjective evaluations. The results show our method can generate solution-driven BID concepts with high quality.