Video Moment Retrieval (VMR) aims to retrieve a specific moment semantically related to the given query. To tackle this task, most existing VMR methods solely focus on the visual and textual modalities while neglecting the complementary but important audio modality. Although a few recent works try to tackle the joint audio-vision-text reasoning, they treat all modalities equally and simply embed them without fine-grained interaction for moment retrieval. These designs are counter-practical as: Not all audios are helpful for video moment retrieval, and the audio of some videos may be complete noise or background sound that is meaningless to the moment determination. To this end, we propose a novel Importance-aware Multi-Granularity fusion model (IMG), which learns to dynamically and selectively aggregate the audio-vision-text contexts for VMR. Specifically, after integrating the textual guidance with vision and audio separately, we first design a pseudo-label-supervised audio importance predictor that predicts the importance score of the audio, and accordingly assigns weights to mitigate the interference caused by noisy audio. Then, we design a multi-granularity audio fusion module that adaptively fuses audio and visual modalities at local-, event-, and global-level, fully capturing their complementary contexts. We further propose a cross-modal knowledge distillation strategy to address the challenge of missing audio modality during inference. To evaluate our method, we further construct a new VMR dataset, i.e., Charades-AudioMatter, where audio-related samples are manually selected and re-organized from the original Charades-STA to validate the model's capability in utilizing audio modality. Extensive experiments validate the effectiveness of our method, achieving state-of-the-art with audio-video fusion in VMR methods. Our code is available at https://github.com/HuiGuanLab/IMG.