Taxonomy induction is crucial for organizing concepts into explicit and interpretable semantic hierarchies. While existing methods have achieved promising results, their generalization, structural reliability, and efficiency remain limited, hindering their performance in zero-shot and large-scale scenarios. To overcome these limitations, we introduce BoostTaxo, a boosting-style LLM framework for zero-shot taxonomy induction. It takes a set of domain terms as inputs and performs parent identification in a coarse-to-fine manner, employing retrieval-augmented definition refinement, hybrid parent candidate selection, candidate rating, and structure-aware score calibration to improve taxonomy construction. Specifically, a lightweight LLM is used to efficiently filter candidate parents, while a large-scale LLM is employed to rank and score candidate parents for fine-grained parent selection. Structural features are further incorporated to calibrate candidate edge weights and enhance the reliability of the induced taxonomy. The unified BoostTaxo is evaluated on three public benchmark datasets, namely WordNet, DBLP, and SemEval-Sci, and achieves superior or comparable performance to state-of-the-art methods in zero-shot taxonomy induction. The ablation study validates the contribution of the hybrid parent candidate selection and the structure-aware score calibration to the overall performance. Further analysis investigates the impact of candidate selection size on taxonomy quality and presents representative case and failure studies, providing deeper insights into the effectiveness and limitations of the proposed framework.