Mobile applications (Apps) could expose children to inappropriate themes such as sexual content, violence, and drug use. Maturity rating offers a quick and effective method for potential users, particularly guardians, to assess the maturity levels of apps. Determining accurate maturity ratings for mobile apps is essential to protect children's health in today's saturated digital marketplace. Existing approaches to maturity rating are either inaccurate (e.g., self-reported rating by developers) or costly (e.g., manual examination). In the literature, there are few text-mining-based approaches to maturity rating. However, each app typically involves multiple modalities, namely app description in the text, and screenshots in the image. In this paper, we present a framework for determining app maturity levels that utilize multimodal large language models (MLLMs), specifically ChatGPT-4 Vision. Powered by Chain-of-Thought (CoT) reasoning, our framework systematically leverages ChatGPT-4 to process multimodal app data (i.e., textual descriptions and screenshots) and guide the MLLM model through a step-by-step reasoning pathway from initial content analysis to final maturity rating determination. As a result, through explicitly incorporating CoT reasoning, our framework enables ChatGPT to understand better and apply maturity policies to facilitate maturity rating. Experimental results indicate that the proposed method outperforms all baseline models and other fusion strategies.