One goal of social recommendation is to utilize social information to alleviate data sparsity and improve recommendation accuracy. User social relationships are inherently graph-structured, graph neural network (GNN) has recently attracted extensive attention in social recommendation because of its capability to integrate structural information and topology. However, current graph neural network (GNN)-based social recommendation models fail to consider context information during user interactions, which hinders more accurate modeling of user interest features. To address this problem, we propose a new social recommendation model based on context-aware graph neural network named CENTRIC (User-ContExt CollaboratioN and TensoR Factorization for GNN-based SocIal ReCommendation). Specifically, first a multi-channel GNN model with user-context collaboration module is designed, so that context can directly affect user features and participate in the calculation of user interaction probability with items. Then tensor factorization is adopted in output layer to effectively fuse the features extracted from different channels. Experiments on three public datasets show that CENTRIC significantly outperforms other state-of-the-art social recommendation models, further experiments also demonstrate that context information and tensor factorization help improve the accuracy of GNN-based social recommendation.