Training AI models has always been challenging, especially when there is a need for custom models to provide personalized services. Algorithm engineers often face a lengthy process to iteratively develop models tailored to specific business requirements, making it even more difficult for non-experts. The quest for high-quality and efficient model development, along with the emergence of Large Language Model (LLM) Agents, has become a key focus in the industry. Leveraging the powerful analytical, planning, and decision-making capabilities of LLM, we propose a TrainerAgent system comprising a multi-agent framework including Task, Data, Model and Server agents. These agents analyze user-defined tasks, input data, and requirements (e.g., accuracy, speed), optimizing them comprehensively from both data and model perspectives to obtain satisfactory models, and finally deploy these models as online service. Experimental evaluations on classical discriminative and generative tasks in computer vision and natural language processing domains demonstrate that our system consistently produces models that meet the desired criteria. Furthermore, the system exhibits the ability to critically identify and reject unattainable tasks, such as fantastical scenarios or unethical requests, ensuring robustness and safety. This research presents a significant advancement in achieving desired models with increased efficiency and quality as compared to traditional model development, facilitated by the integration of LLM-powered analysis, decision-making, and execution capabilities, as well as the collaboration among four agents. We anticipate that our work will contribute to the advancement of research on TrainerAgent in both academic and industry communities, potentially establishing it as a new paradigm for model development in the field of AI.