Large language models (LLMs) have demonstrated astonishing capabilities in natural language processing (NLP) tasks, sparking interest in their application to professional domains with higher specialized requirements. However, restricted access to closed-source LLMs via APIs and the difficulty in collecting massive high-quality datasets pose obstacles to the development of large language models in education fields of various courses. Given these challenges, we propose CourseGPT-zh, a course-oriented education LLM that supports customization and low-cost deployment. To address the comprehensiveness and diversity requirements of course-specific corpora, we design a high-quality question-answering corpus distillation framework incorporating prompt optimization, which effectively mines textbook knowledge and enhances its diversity. Moreover, considering the alignment of LLM responses with user needs, a novel method for discrete prompt optimization based on LLM-as-Judge is introduced. During optimization, this framework leverages the LLM's ability to reflect on and exploit error feedback and patterns, allowing for prompts that meet user needs and preferences while saving response length. Lastly, we obtain CourseGPT-zh based on the open-source LLM using parameter-efficient fine-tuning. Experimental results show that our discrete prompt optimization framework effectively improves the response quality of ChatGPT, and CourseGPT-zh exhibits strong professional capabilities in specialized knowledge question-answering, significantly outperforming comparable open-source models.