Domain-Specific Chinese Relation Extraction (DSCRE) aims to extract relations between entities from domain-specific Chinese text. Despite the rapid development of PLMs in recent years, especially LLMs, DSCRE still faces three core challenges: complex network structure design, poor awareness, and high consumption of fine-tuning. Given the impressive performance of large language models (LLMs) in natural language processing, we propose a new framework called CRE-LLM. This framework is based on fine-tuning open-source LLMs, such as Llama-2, ChatGLM2, and Baichuan2. CRE-LLM enhances the logic-awareness and generative capabilities of the model by constructing an appropriate prompt and utilizing open-source LLMs for instruction-supervised fine-tuning. And then it directly extracts the relations of the given entities in the input textual data, which improving the CRE approach. To demonstrate the effectiveness of the proposed framework, we conducted extensive experiments on two domain-specific CRE datasets, FinRE and SanWen. The experimental results show that CRE-LLM is significantly superior and robust, achieving state-of-the-art (SOTA) performance on the FinRE dataset. This paper introduces a novel approach to domain-specific relation extraction (DSCRE) tasks that are semantically more complex by combining LLMs with triples. Our code is publicly available.