Resume matching is a crucial task in human resource management, where the goal is to find the most suitable candidates for a job by comparing their resumes against job descriptions. Traditional approaches rely on classical natural language processing (NLP) techniques and machine learning models, but the recent advent of quantum computing has opened new avenues for solving such problems with enhanced efficiency. In this paper, we propose a hybrid quantum-classical model for job resume matching. The classical part involves text processing using TF-IDF vectorization, while the quantum component leverages quantum feature mapping and quantum circuits to evaluate the similarity between job descriptions and resumes. The proposed method is tested on a synthetic dataset of 100 job descriptions and resumes, showing competitive results compared to classical methods. This study demonstrates the potential of hybrid quantum models in real-world applications, particularly in HR systems.