The widespread use of deep learning technology across various industries has made deep neural network models highly valuable and, as a result, attractive targets for potential attackers. Model extraction attacks, particularly query-based model extraction attacks, allow attackers to replicate a substitute model with comparable functionality to the victim model and present a significant threat to the confidentiality and security of MLaaS platforms. While many studies have explored threats of model extraction attacks against classification models in recent years, object detection models, which are more frequently used in real-world scenarios, have received less attention. In this paper, we investigate the challenges and feasibility of query-based model extraction attacks against object detection models and propose an effective attack method called MEAOD. It selects samples from the attacker-possessed dataset to construct an efficient query dataset using active learning and enhances the categories with insufficient objects. We additionally improve the extraction effectiveness by updating the annotations of the query dataset. According to our gray-box and black-box scenarios experiments, we achieve an extraction performance of over 70% under the given condition of a 10k query budget.