Given the wide application of 3D model analysis, covering domains such as medicine, engineering, and virtual reality, the demand for innovative content-based 3D shape retrieval systems capable of handling complex 3D data efficiently have significantly increased. This paper proposes a new 3D shape retrieval method that uses the CatBoost classifier, a machine learning algorithm, to capture a unique descriptor for each 3D mesh. The main idea of our method is to get a specific and a unique signature or descriptor for each 3D model by training the CatBoost classifier with features obtained directly from the 3D models. This idea not only accelerates the training process, but also ensures the consistency and relevance of the data fed to the classifier during the training process. Once fully trained, the classifier generates a descriptor that is used during the indexing and retrieval process. The efficiency of our method is demonstrated by conducting extensive experiments on the Princeton shape benchmark database. The results demonstrate high retrieval accuracy in comparison to various existing methods in the literature. Our method's ability to outperform these methods shows its potential as highly useful tool in the field of content-based 3D shape retrieval.