To enhance the effectiveness of the Advanced Persistent Threat (APT) detection process, this research proposes a new approach to build and analyze the behavior profiles of APT attacks in network traffic. To achieve this goal, this study carries out two main objectives, including (i) building the behavior profile of APT IP in network traffic using a new intelligent computation method; (ii) analyzing and evaluating the behavior profile of APT IP based on a deep graph network. Specifically, to build the behavior profile of APT IP, this article describes using a combination of two different data mining methods: Bidirectional Long Short-Term Memory (Bi) and Attention (A). Based on the obtained behavior profile, the Dynamic Graph Convolutional Neural Network (DGCNN) is proposed to extract the characteristics of APT IP and classify them. With the flexible combination of different components in the model, the important information and behavior of APT attacks are demonstrated, not only enhancing the accuracy of detecting attack campaigns but also reducing false predictions. The experimental results in the paper show that the method proposed in this study has brought better results than other approaches on all measurements. In particular, the accuracy of APT attack prediction results (Precision) reached from 84 to 91%, higher than other studies of over 7%. These experimental results have proven that the proposed BiADG model for detecting APT attacks in this study is proper and reasonable. In addition, those experimental results have not only proven the effectiveness and superiority of the proposed method in detecting APT attacks but have also opened up a new approach for other cyber-attack detections such as distributed denial of service, botnets, malware, phishing, etc.