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Few-shot Out-of-Distribution (OOD) detection has emerged as a critical research direction in machine learning for practical deployment. Most existing Few-shot OOD detection methods suffer from insufficient generalization capability for the open world. Due to the few-shot learning paradigm, the OOD detection ability is often overfit to the limited training data itself, thus degrading the performance on generalized data and performing inconsistently across different scenarios. To address this challenge, we proposed a Generalized Few-shot OOD Detection (GOOD) framework, which empowers the general knowledge of the OOD detection model with an auxiliary General Knowledge Model (GKM), instead of directly learning from few-shot data. We proceed to reveal the few-shot OOD detection from a generalization perspective and theoretically derive the Generality-Specificity balance (GS-balance) for OOD detection, which provably reduces the upper bound of generalization error with a general knowledge model. Accordingly, we propose a Knowledge Dynamic Embedding (KDE) mechanism to adaptively modulate the guidance of general knowledge. KDE dynamically aligns the output distributions of the OOD detection model to the general knowledge model based on the Generalized Belief (G-Belief) of GKM, thereby boosting the GS-balance. Experiments on real-world OOD benchmarks demonstrate our superiority. Codes will be available.