Blockchain technology is a popular solution for secure transactions in untrusted networks. However, with the growing number of blockchain applications, how to ensure the security of the blockchain system itself has become an urgent problem. In this paper, we propose a novel security-testing framework for blockchain systems based on a vulnerability-detection model. Our study involves an analysis and comparison with existing software-vulnerability analysis methods. Our framework first addresses each factor that impacts the security of the blockchain system, with a vulnerability attack graph being constructed using model-checking to describe the complete exploitation process of system vulnerabilities. Reliability Theory is used to quantitatively assess the vulnerability attack graph of the blockchain system, thereby providing a theoretical basis for evaluating its security. Finally, we verify the effectiveness and feasibility of the proposed security-testing framework for blockchain systems on an e-voting election blockchain system. The results from our extensive experiments show that our proposed method outperforms other formal-verification-based methods for detecting blockchain vulnerabilities, and also provides a scientific and reliable assessment of blockchain system security.