As a popular task in graph learning, node classification seeks to assign labels to nodes, taking into account both their features and connections. However, an important challenge for its application in real-world scenarios is the presence of newly-emerged out-of-distribution samples and noisy samples, which affect the quality and robustness of learned classifiers. Out-of-distribution (OOD) samples are often found in both the training and testing phases. Such samples don't belong to any known categories. These OOD samples are considered as outliers (OOD noise) when they appear during training, and are recognized as open-set samples during the testing. Meanwhile, in-distribution (IND) noisy data, i.e., known class samples with wrong labels, are also prevalent and inevitably degrade a model's performance. The challenge of open-set learning with complex IND and OOD noise remains largely unexplored, particularly when dealing with non-IID graph data. To address these challenges, this paper introduces a novel complex-noise-resistant open-set node classification approach, designed for open-set graph data containing both IND and OOD noisy nodes. Specifically, a trustworthiness learner is adopted to learn the trustworthiness rates of the feature and label for each node while a decoder and an open-set classifier are trained to reconstruct the structure of a node and to predict its category simultaneously with the guidance of node trustworthiness. The experimental results demonstrate the superiority of our method.