Graph neural networks (GNNs) have achieved strong performance in various applications. In the real world, network data is usually formed in a streaming fashion. The distributions of patterns that refer to neighborhood information of nodes may shift over time. The GNN model needs to learn the new patterns that cannot yet be captured. But learning incrementally leads to the catastrophic forgetting problem that historical knowledge is overwritten by newly learned knowledge. Therefore, it is important to train GNN model to learn new patterns and maintain existing patterns simultaneously, which few works focus on. In this paper, we propose a streaming GNN model based on continual learning so that the model is trained incrementally and up-to-date node representations can be obtained at each time step. Firstly, we design an approximation algorithm to detect new coming patterns efficiently based on information propagation. Secondly, we combine two perspectives of data replaying and model regularization for existing pattern consolidation. Specially, a hierarchy-importance sampling strategy for nodes is designed and a weighted regularization term for GNN parameters is derived, achieving greater stability and generalization of knowledge consolidation. Our model is evaluated on real and synthetic data sets and compared with multiple baselines. The results of node classification prove that our model can efficiently update model parameters and achieve comparable performance to model retraining. In addition, we also conduct a case study on the synthetic data, and carry out some specific analysis for each part of our model, illustrating its ability to learn new knowledge and maintain existing knowledge from different perspectives.