Graph neural networks (GNNs) based on message passing have achieved remarkable performance in (semi-supervised) node classification. However, most existing works assume that node labels are noise-free, while the learning errors on mislabeled nodes can be easily propagated to unlabeled nodes along the graph structure. In this paper, we perform a preliminary study showing that message passing can potentially hurt the performance of GNN-based node classification with the existence of label noise. To address this issue, we propose to decouple the processes of message passing and node classification. Specifically, we first train a message-passing GNN in a self-supervised manner to learn informative node representations. Next, we propose a novel topology-aware noise transition matrix estimation algorithm to learn a robust node classifier without using GNNs. We conduct extensive experiments on real-world datasets for semi-supervised node classification with different levels of class-dependent and instance-dependent label noise and show new state-of-the-art performance.