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. In this phenomenon, LLMs either omit (neglecting to address certain parts) or misinterpret (responding to invented query parts) elements of the given query, leading to intent hallucinated generation. 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) the phenomenon stems from omission or misinterpretation of LLMs. To facilitate future research, we introduce an automatic LLM generation evaluation metric, CONSTRAINT SCORE, for detecting intent hallucination. Human evaluation results demonstrate that CONSTRAINT SCORE is closer to human performance for intent hallucination compared to baselines.