With the proliferation of Web services, it is very difficult for inexperienced users to select the most appropriate service among numerous functionally identical or similar candidates, thus prediction of Quality of Service (QoS) becomes a growing concern in service discovery, selection and recommendation. However, a huge challenge is that in the reality of the existence of untrustworthy users, how the Web service recommendation system keeps the robustness of the QoS prediction while maintaining high accuracy. To address this problem, a Reputation Integrated Graph Convolution Network (RIGCN) is developed in this paper to realize robust and accurate QoS prediction. RIGCN has three main parts: Reputation Extraction, Multi-source Feature Extraction and GCN-based QoS Prediction. First, an Outlier and Pattern Measure (OPM) method is proposed to extract the real reputation of users based on both outliers and the distribution patterns of the historical QoS interaction records. Second, deep features of users and services are captured by multi-source feature extraction with an attention mechanism to make full use of the contextual information in service invocation. On this basis, a graph convolution network is specially designed to integrate multi-source features and user reputation in the message propagation process to complete final QoS prediction. Experimental results demonstrate that our RIGCN approach can not only extract and utilize implicit and explicit features of various multi-source data, but also can reduce the negative influence of untrustworthy users. Therefore, it is very robust and effective in improving the accuracy of QoS prediction with sparse and noisy data.