Optimization problems seek to find the best solution to an objective under a set of constraints, and have been widely investigated in real-world applications. Modeling and solving optimization problems in a specific domain typically require a combination of domain knowledge, mathematical skills, and programming ability, making it difficult for general users and even domain professionals. In this paper, we propose a novel framework called OptLLM that augments LLMs with external solvers. Specifically, OptLLM accepts user queries in natural language, convert them into mathematical formulations and programming codes, and calls the solvers to calculate the results for decision-making. In addition, OptLLM supports multi-round dialogues to gradually refine the modeling and solving of optimization problems. To illustrate the effectiveness of OptLLM, we provide tutorials on three typical optimization applications and conduct experiments on both prompt-based GPT models and a fine-tuned Qwen model using a large-scale self-developed optimization dataset. Experimental results show that OptLLM works with various LLMs, and the fine-tuned model achieves an accuracy boost compared to the prompt-based models. Some features of OptLLM framework have been available for trial since June 2023 (https://opt.alibabacloud.com/chat or https://opt.aliyun.com/chat).