Anomalies in business processes are inevitable for various reasons such as system failures and operator errors. Detecting anomalies is important for the management and optimization of business processes. In this paper, we propose a multi-Graph based Anomaly detection fraMework for business processes via grAph neural networks, named GAMA. GAMA  makes use of structural process information and attribute information in a more integrated way. In GAMA,  multiple graphs are applied to model a trace in which each attribute is modelled as a separate  graph.  In particular, the graph constructed for the special attribute activity reflects the control flow. Then GAMA employs  a multi-graph encoder and a multi-sequence decoder on multiple graphs  to detect anomalies in terms of the reconstruction errors.  Moreover, three teacher forcing styles are designed to enhance GAMA’s ability to reconstruct normal behaviours  and thus improve detection performance. We  conduct extensive experiments on both synthetic logs and real-life logs. The experiment results demonstrate that GAMA outperforms state-of-the-art methods for both trace-level and attribute-level anomaly detection.