Meta-learning, or learning to learn, is a technique that can help to overcome resource scarcity in cross-lingual NLP problems, by enabling fast adaptation to new tasks. We apply model-agnostic meta-learning (MAML) to the task of cross-lingual dependency parsing. We train our model on a diverse set of languages to learn a parameter initialization that can adapt quickly to new languages. We find that meta-learning with pre-training can significantly improve upon the performance of language transfer and standard supervised learning baselines for a variety of unseen, typologically diverse, and low-resource languages, in a few-shot learning setup.