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Recognizing multiple labels of an image is a practical yet challenging task, and remarkable progress has been achieved by searching for semantic regions and exploiting label dependencies. However, current works utilize RNN/LSTM to implicitly capture sequential region/label dependencies, which cannot fully explore mutual interactions among the semantic regions/labels and do not explicitly integrate label co-occurrences. In addition, these works require large amounts of training samples for each category, and they are unable to generalize to novel categories with limited samples. To address these issues, we propose a knowledge-guided graph routing (KGGR) framework, which unifies prior knowledge of statistical label correlations with deep neural networks. The framework exploits prior knowledge to guide adaptive information propagation among different categories to facilitate multi-label analysis and reduce the dependency of training samples. Specifically, it first builds a structured knowledge graph to correlate different labels based on statistical label co-occurrence. Then, it introduces the label semantics to guide learning semantic-specific features to initialize the graph, and it exploits a graph propagation network to explore graph node interactions, enabling learning contextualized image feature representations. Moreover, we initialize each graph node with the classifier weights for the corresponding label and apply another propagation network to transfer node messages through the graph. In this way, it can facilitate exploiting the information of correlated labels to help train better classifiers. We conduct extensive experiments on the traditional multi-label image recognition (MLR) and multi-label few-shot learning (ML-FSL) tasks and show that our KGGR framework outperforms the current state-of-the-art methods by sizable margins on the public benchmarks.