To address the challenges of traditional knowledge graph construction (KGC) methods, this paper proposes a framework AdaOntoKG that combines ontology-driven and adaptive chain-of-thought reasoning (Adaptive CoT). The framework builds and expands domain ontologies with LLMs, and guides triple extraction through Zero-Shot-CoT and Few-Shot-CoT, with ontology constraints ensuring semantic consistency and structural validity. Experiments on multiple benchmarks show that AdaOntoKG outperforms mainstream baselines in F1 and AUC, while achieving high ontology conformance. Overall, AdaOntoKG enhances accuracy, controllability, and domain adaptability, providing a scalable solution for constructing high-quality knowledge graphs.