In a conversational system, dynamically generating follow-up questions based on context can help users explore information and provide a better user experience. Humans are usually able to ask questions that involve some general life knowledge and demonstrate higher order cognitive skills. However, the questions generated by existing methods are often limited to shallow contextual questions that are uninspiring and have a large gap to the human level. In this paper, we propose a three-stage external knowledge-enhanced follow-up question generation method, which generates questions by identifying contextual topics, constructing a knowledge graph (KG) online, and finally combining these with a large language model to generate the final question. The model generates information-rich and exploratory follow-up questions by introducing external common sense knowledge and performing a knowledge fusion operation. Experiments show that compared to baseline models, our method generates questions that are more informative and closer to human questioning levels while maintaining contextual relevance.