With the development of the Internet, the recommendation based on Quality of Service(QoS) is proven to be an efficient way to deal with the ever-increasing web services in both industry and academia. However, it is hard to make an accurate recommendation using sparse QoS data, which makes QoS prediction a growing concern in the context of web service recommendation. In this research, a novel Graph-based Matrix Factorization approach(GMF) is proposed for QoS prediction. First, a concept of integrated-graph is put forward to consolidate multi-source information from user–aware context and service-aware context, and to deep mine potential relationships based on QoS matrix. Furthermore, the integrated-graph is divided into several sub-graphs by cutting insignificant edges to reduce noises and strengthen interactions between users and services. Based on the local information of each sub-graph and the global information of integrated-graph, a Gaussian Mixture Model(GMM) of QoS value is built as a fusion method to combine local and global information adaptively and to complete final QoS prediction. The extensive experimental analysis on a publicly available dataset indicate that our graph-based method is both accurate and practical.