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Dynamic facial expression recognition (FER) databases provide important data support for affective computing and applications. However, most FER databases are annotated with several basic mutually exclusive emotional categories and contain only one modality, e.g., videos. The monotonous labels and modality cannot accurately imitate human emotions and fulfill applications in the real world. In this paper, we propose MAFW, a large-scale multi-modal compound affective database with 10,045 video-audio clips in the wild. Each clip is annotated with a compound emotional category and a couple of sentences that describe the subjects' affective behaviors in the clip. For the compound emotion annotation, each clip is categorized into one or more of the 11 widely-used emotions, i.e., anger, disgust, fear, happiness, neutral, sadness, surprise, contempt, anxiety, helplessness, and disappointment. To ensure high quality of the labels, we filter out the unreliable annotations by an Expectation Maximization (EM) algorithm, and then obtain 11 single-label emotion categories and 32 multi-label emotion categories. To the best of our knowledge, MAFW is the first in-the-wild multi-modal database annotated with compound emotion annotations and emotion-related captions. Additionally, we also propose a novel Transformer-based expression snippet feature learning method to recognize the compound emotions leveraging the expression-change relations among different emotions and modalities. Extensive experiments on MAFW database show the advantages of the proposed method over other state-of-the-art methods for both uni- and multi-modal FER. Our MAFW database is publicly available from https://mafw-database.github.io/MAFW.