Abstract: Sentence function is an important linguistic feature indicating the communicative purpose in uttering a sentence. Incorporating sentence functions into conversations has shown improvements in the quality of generated responses. However, the number of utterances for different types of fine-grained sentence functions is extremely imbalanced. Besides a small number of high-resource sentence functions, a large portion of sentence functions is infrequent. Consequently, dialogue generation conditioned on these infrequent sentence functions suffers from data deficiency. In this paper, we investigate a structured meta-learning (SML) approach for dialogue generation on infrequent sentence functions. We treat dialogue generation conditioned on different sentence functions as separate tasks, and apply model-agnostic meta-learning to high-resource sentence functions data. Furthermore, SML enhances meta-learning effectiveness by promoting knowledge customization among different sentence functions but simultaneously preserving knowledge generalization for similar sentence functions. Experimental results demonstrate that SML not only improves the informativeness and relevance of generated responses, but also can generate responses consistent with the target sentence functions. Code will be public to facilitate the research along this line.