Contactless fingerprint recognition has attracted increasing attention because of its higher data safety and hygiene than traditional contact-based fingerprints. However, accurate matching of contactless fingerprints is still challenging due to the inevitable perspective distortions and variations of illumination and poses. Traditional matching methods are mainly based on minutiae topology and hand-designed descriptors, which cannot work well on contactless fingerprints. Towards more accurate matching of contactless fingerprints, this paper proposes a deep geometric graph neural network to jointly learn the multi-level minutia features and their similarities in an end-to-end fashion. First, given a set of minutia points, a convolutional neural network is built on fingerprint images to extract the low level features of minutiae. Second, we propose a geometric graph neural network with minutia points as nodes and the adjacent minutiae connected with edges, which can pass and aggregate messages of minutia nodes to learn the high level geometric features. Third, minutia matching is converted into binary classification problem with a focal loss function to learn the similarity of minutia pairs. Finally, fingerprint matching is performed by integrating the similarities of matched minutia pairs. Our method is tested on contactless fingerprints from two public datasets and one wet dataset collected in our laboratory. Experimental results show that our method performs better than other state-of-the-art methods for contactless fingerprint matching.