Large Language Models (LLMs) have shown impressive capabilities but still suffer from the issue of hallucinations. A significant type of this issue is the false premise hallucination, which we define as the phenomenon when LLMs generate hallucinated text when confronted with false premise questions. In this paper, we perform a comprehensive analysis of the false premise hallucination and elucidate its internal working mechanism: a small subset of attention heads (which we designate as false premise heads) disturb the knowledge extraction process, leading to the occurrence of false premise hallucination. Based on our analysis, we propose \textbf{FAITH} (\textbf{F}alse premise \textbf{A}ttention head constra\textbf{I}ining for mi\textbf{T}igating \textbf{H}allucinations), a novel and effective method to mitigate false premise hallucinations. It constrains the false premise attention heads during the model inference process. Impressively, extensive experiments demonstrate that constraining only approximately $1\%$ of the attention heads in the model yields a notable increase of nearly $20\%$ of model performance.