Abstract: Tree-search-based reasoning methods have significantly enhanced the reasoning capability of large language models (LLMs) by facilitating the exploration of multiple intermediate reasoning steps, i.e., thoughts. However, these methods suffer from substantial inference latency, as they have to generate numerous reasoning thoughts, severely limiting LLM applicability. To address this challenge, we propose a novel Speculative Search (SpecSearch) framework that significantly accelerates LLM reasoning by optimizing thought generation. Specifically, SpecSearch utilizes a small model to strategically collaborate with a large model at both thought and token levels, efficiently generating high-quality reasoning thoughts. The major pillar of SpecSearch is a novel quality-preserving rejection mechanism, which effectively filters out thoughts whose quality falls below that of the large model's outputs. Moreover, we show that SpecSearch preserves comparable reasoning quality to the large model. Experiments on both the Qwen and Llama models demonstrate that SpecSearch significantly outperforms state-of-the-art approaches, achieving up to 2.12$\times$ speedup with comparable reasoning quality.