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Most existing compound facial expression recognition (FER) methods rely on large-scale labeled compound expression data for training. However, collecting such data is labor-intensive and time-consuming. In this paper, we address the compound FER task in the cross-domain few-shot learning (FSL) setting, which requires only a few samples of compound expressions in the target domain. Specifically, we propose a novel cascaded decomposition network (CDNet), which cascades several learn-to-decompose modules with shared parameters based on a sequential decomposition mechanism, to obtain a transferable feature space. To alleviate the overfitting problem caused by limited base classes in our task, a partial regularization strategy is designed to effectively exploit the best of both episodic training and batch training. By training across similar tasks on multiple basic expression datasets, CDNet learns the ability of learn-to-decompose that can be easily adapted to identify unseen compound expressions. Extensive experiments on both in-the-lab and in-the-wild compound expression datasets demonstrate the superiority of our proposed CDNet against several state-of-the-art FSL methods. Code is available at: https://github.com/zouxinyi0625/CDNet.