Large vision-language models (LVLMs) have achieved remarkable performance on multimodal tasks such as visual question answering (VQA) and image captioning. However, they still suffer from hallucinations, generating text inconsistent with visual input, posing significant risks in real-world applications. Existing approaches to address this issue focus on incorporating external knowledge bases, alignment training, or decoding strategies, all of which require substantial computational cost and time. Recent works try to explore more efficient alternatives by adjusting LVLMs' internal representations. Although promising, these methods may cause hallucinations to be insufficiently suppressed or lead to excessive interventions that negatively affect normal semantics. In this work, we leverage sparse autoencoders (SAEs) to identify semantic directions closely associated with either hallucinations or actuality, realizing more precise and direct hallucination-related representations. Our analysis demonstrates that interventions along the faithful direction we identified can mitigate hallucinations, while those along the hallucinatory direction can exacerbate them. Building on these insights, we propose Steering LVLMs via SAE Latent Directions (SSL), a training-free method based on SAE-derived latent directions to mitigate hallucinations in LVLMs. Extensive experiments demonstrate that SSL significantly outperforms existing decoding approaches in mitigating hallucinations, while maintaining transferability across different model architectures with negligible additional time overhead.