The automation of resume screening is a crucial aspect of the recruitment process in organizations. Automated resume screening systems often encompass a range of natural language processing (NLP) tasks. The advent of Large Language Models (LLMs) has notably enhanced the efficacy of these systems, showcasing their robust generalization abilities across diverse language-related tasks. Accompanying these developments are various agents based on LLMs, which facilitate their application in practical scenarios. This paper introduces a novel LLM-based agent framework for resume screening, aimed at enhancing efficiency and time management in recruitment processes. Our framework is distinct in its ability to efficiently summarize and grade each resume from a large dataset. Moreover, it utilizes LLM agents for decision-making, determining which candidates receive job offers, or which ones to bring in for interviews. To evaluate our framework, we constructed a dataset from actual resumes and conducted simulate a resume screening process. Subsequently, the outcomes of the simulation experiment were compared and subjected to detailed analysis. The results demonstrate that our automated resume screening framework is 11 times faster than traditional manual methods. Furthermore, by fine-tuning the LLMs, we observed a significant improvement in the F1 score, reaching 87.73\%, during the resume sentence classification phase. In the resume summarization and grading phase, our fine-tuned model surpassed the baseline performance of the GPT-3.5 model. Analysis of the decision-making efficacy of the LLM agents in the final offer stage further underscores the potential of LLM agents in transforming resume screening processes.