Microservice architecture has sprung up over recent years for managing enterprise applications, due to its ability to independently deploy and scale services. Despite its benefits, ensuring the reliability and safety of a microservice system remains highly challenging. Existing anomaly detection algorithms based on a single data modality (i.e., metrics, logs, or traces) fail to fully account for the complex correlations and interactions between different modalities, leading to false negatives and false alarms, whereas incorporating more data modalities can offer opportunities for further performance gain. As a fresh attempt, we propose in this paper a semi-supervised graph-based anomaly detection method, MSTGAD, which seamlessly integrates all available data modalities via attentive multi-modal learning. First, we extract and normalize features from the three modalities, and further integrate them using a graph, namely MST (microservice system twin) graph, where each node represents a service instance and the edge indicates the scheduling relationship between different service instances. The MST graph provides a virtual representation of the status and scheduling relationships among service instances of a real-world microservice system. Second, we construct a transformer-based neural network with both spatial and temporal attention mechanisms to model the inter-correlations between different modalities and temporal dependencies between the data points. This enables us to detect anomalies automatically and accurately in real-time. Extensive experiments on two real-world datasets verify the effectiveness of our proposed MSTGAD method, achieving competitive performance against state-of-the-art approaches, with a 0.961 F1-score and an average increase of 4.85%. The source code of MST-GAD is publicly available at https://github.com/ant-research/microservice_system_twin_graph_based_anomaly_detection.