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. This paper introduces a novel Large Language Models (LLMs) 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. To evaluate our framework, we constructed a dataset from actual resumes and simulated 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.