The Finite Element Method (FEM) is widely used in engineering and scientific computing, but its pre-processing, solver configuration, and post-processing stages are often time-consuming and require specialized knowledge. This paper proposes an automated solution framework, MooseAgent, for the multi-physics simulation framework MOOSE, which combines large-scale pre-trained language models (LLMs) with a multi-agent system. The framework uses LLMs to understand user-described simulation requirements in natural language and employs task decomposition and multi-round iterative verification strategies to automatically generate MOOSE input files. To improve accuracy and reduce model hallucinations, the system builds and utilizes a vector database containing annotated MOOSE input cards and function documentation. We conducted experimental evaluations on several typical cases, including heat transfer, mechanics, phase field, and multi-physics coupling. The results show that MooseAgent can automate the MOOSE simulation process to a certain extent, especially demonstrating a high success rate when dealing with relatively simple single-physics problems. The main contribution of this research is the proposal of a multi-agent automated framework for MOOSE, which validates its potential in simplifying finite element simulation processes and lowering the user barrier, providing new ideas for the development of intelligent finite element simulation software. The code for the MooseAgent framework proposed in this paper has been open-sourced and is available at https://github.com/taozhan18/MooseAgent