Graph Neural Networks (GNNs) have emerged as a powerful tool for semi-supervised node classification tasks. However, recent studies have revealed various biases in GNNs stemming from both node features and graph topology. In this work, we uncover a new bias - label position bias, which indicates that the node closer to the labeled nodes tends to perform better. We introduce a new metric, the Label Proximity Score, to quantify this bias, and find that it is closely related to performance disparities. To address the label position bias, we propose a novel optimization framework for learning a label position unbiased graph structure, which can be applied to existing GNNs. Extensive experiments demonstrate that our proposed method not only outperforms backbone methods but also significantly mitigates the issue of label position bias in GNNs.