Composed Image Retrieval (CIR) aims to retrieve target images from candidate set using a hybrid-modality query consisting of a reference image and a relative caption that describes the user intent. Recent studies attempt to utilize Vision-Language Pre-training Models (VLPMs) with various fusion strategies for addressing the task.However, these methods typically fail to simultaneously meet two key requirements of CIR: comprehensively extracting visual information and faithfully following the user intent. In this work, we propose CIR-LVLM, a novel framework that leverages the large vision-language model (LVLM) as the powerful user intent-aware encoder to better meet these requirements. Our motivation is to explore the advanced reasoning and instruction-following capabilities of LVLM for accurately understanding and responding the user intent. Furthermore, we design a novel hybrid intent instruction module to provide explicit intent guidance at two levels: (1) The task prompt clarifies the task requirement and assists the model in discerning user intent at the task level. (2) The instance-specific soft prompt, which is adaptively selected from the learnable prompt pool, enables the model to better comprehend the user intent at the instance level compared to a universal prompt for all instances. CIR-LVLM achieves state-of-the-art performance across three prominent benchmarks with acceptable inference efficiency. We believe this study provides fundamental insights into CIR-related fields.