In an era where social media platforms abound, individuals frequently share images that offer insights into their intents and interests, impacting individual life quality and societal stability. Traditional computer vision tasks, such as object detection and semantic segmentation, focus on concrete visual representations, while intent recognition relies more on implicit visual clues. This poses challenges due to the wide variation and subjectivity of such clues, compounded by the problem of intra-class variety in conveying abstract concepts, e.g. "enjoy life". Existing methods seek to solve the problem by manually designing representative features or building prototypes for each class from global features. However, these methods still struggle to deal with the large visual diversity of each intent category. In this paper, we introduce a novel approach named Multi-grained Compositional visual Clue Learning (MCCL) to address these challenges for image intent recognition. Our method leverages the systematic compositionality of human cognition by breaking down intent recognition into visual clue composition and integrating multi-grained features. We adopt class-specific prototypes to alleviate data imbalance. We treat intent recognition as a multi-label classification problem, using a graph convolutional network to infuse prior knowledge through label embedding correlations. Demonstrated by a state-of-the-art performance on the Intentonomy and MDID datasets, our approach advances the accuracy of existing methods while also possessing good interpretability. Our work provides an attempt for future explorations in understanding complex and miscellaneous forms of human expression.