When exposed to complex queries containing multiple conditions, today’s large language models (LLMs) tend to produce responses that only partially satisfy the query while neglecting certain conditions. We, therefore, introduce the concept of Intent Hallucination, a phenomenon where LLMs either omit (failing to address certain parts) or misinterpret (responding to invented query parts) elements of the given query, leading to responses misaligned with the original query. To systematically evaluate intent hallucination, we introduce FAITHQA, a novel benchmark for intent hallucination that contains 20,068 problems, covering both query-only and retrieval-augmented generation (RAG) setups with varying topics and difficulty. FAITHQA is the first hallucination benchmark that goes beyond factual verification, tailored to identify the fundamental cause of intent hallucination. By evaluating various LLMs on FAITHQA, we find that (1) intent hallucination is a common issue even for state-of-the-art models, and (2) such a phenomenon stems from omission or misinterpretation of LLMs. To facilitate future research, we introduce an automatic LLM generation evaluation metric, named INTENT CONSTRAINT, for detecting intent hallucination. Human evaluation results demonstrate that INTENT CONSTRAINT is closer to human performance for intent hallucination compared to baselines.