Abstract: Cloud computing is developing rapidly, and the trustiness of cloud platform is the key issue relating to its success or failure. The authentication of the trustiness of user behavior is an important part of ensuring the credibility of cloud platform. In order to solve the problem of trustiness of cloud users’ behaviors, a cloud user behavior authentication model based on multi-partite graphs (BAM) is proposed. It includes the layer of user behavior evidence, the layer of building behavior multi-partite graphs and the layer of behavior authentication. The behavior evidence is the basis, the multi-partite graphs is the method and the behavior authentication is the purpose. In the layer of user behavior evidence, the model determines the type of evidence, collects behavior evidences and analyzes user behavior quantitatively; in the layer of building behavior multi-partite graphs, the model builds two multi-partite graphs based on the layer of behavior evidence and the knowledge of graph theory; in the layer of behavior authentication, the model builds the cloud user behavior authentication module to verify that users are trusted. Identity re-certification and risk game are introduced to enhance security and accuracy of the model. The analysis of small-scale cloud user behaviors in simulation experiments show that, the model is accurate and effective in measuring the normal behavior of cloud users and in distinguishing malicious user with the risk user, and it has higher detection ratio and lower false positive ratio.