Node classification is a fundamental graph-based task that aims to predict the classes of unlabeled nodes, for which Graph Neural Networks (GNNs) are the state-of-the-art methods. Current GNNs assume that nodes in the training set contribute equally during training. However, the quality of training nodes varies greatly, and the performance of GNNs could be harmed by two types of low-quality training nodes: (1) inter-class nodes situated near class boundaries that lack the typical characteristics of their corresponding classes. Because GNNs are data-driven approaches, training on these nodes could degrade the accuracy. (2) mislabeled nodes. In real-world graphs, nodes are often mislabeled, which can significantly degrade the robustness of GNNs. To mitigate the detrimental effect of the low-quality training nodes, we present CLNode, which employs a selective training strategy to train GNN based on the quality of nodes. Specifically, we first design a multi-perspective difficulty measurer to accurately measure the quality of training nodes. Then, based on the measured qualities, we employ a training scheduler that selects appropriate training nodes to train GNN in each epoch. To evaluate the effectiveness of CLNode, we conduct extensive experiments by incorporating it in six representative backbone GNNs. Experimental results on real-world networks demonstrate that CLNode is a general framework that can be combined with various GNNs to improve their accuracy and robustness.