Software vulnerabilities have posed huge threats to the cyberspace security, and there is an increasing demand for automated vulnerability detection (VD). In recent years, deep learning-based (DL-based) vulnerability detection systems have been proposed for the purpose of automatic feature extraction from source code. Although these methods can achieve ideal performance on synthetic datasets, the accuracy drops a lot when detecting real-world vulnerability datasets. Moreover, these approaches limit their scopes within a single function, being not able to leverage the information between functions. In this paper, we attempt to extract the function’s abstract behaviors, figure out the relationships between functions, and use this global information to assist DL-based VD to achieve higher performance. To this end, we build a behavior graph model and use it to design a novel framework, namely VulBG. To examine the ability of our constructed behavior graph model, we choose several existing DL-based VD models (e.g., TextCNN, ASTGRU, CodeBERT, Devign, and VulCNN) as our baseline models and conduct evaluations on two real-world datasets: the balanced FFMpeg+Qemu dataset and the unbalanced Chrome+Debian dataset. Experimental results indicate that VulBG enables all baseline models to detect more real vulnerabilities, thus improving the overall detection performance.