In this paper, a new relation network based approach to curved text detection is proposed by formulating it as a visual relationship detection problem. The key idea is to decompose curved text detection into two subproblems, namely detection of text primitives and prediction of link relationship for each nearby text primitive pair. Specifically, an anchor-free region proposal network based text detector is first used to detect text primitives of different scales from different feature maps of a feature pyramid network, from which a manageable number of text primitive pairs are selected. Then, a relation network is used to predict whether each text primitive pair belongs to a same text instance. Finally, isolated text primitives are grouped into curved text instances based on link relationships of text primitive pairs. Because pairwise link prediction has used features extracted from the bounding boxes of each text primitive and their union, the relation network can effectively leverage wider context information to improve link prediction accuracy. Furthermore, since the link relationships of relatively distant text primitives can be predicted robustly, our relation network based text detector is capable of detecting text instances with large inter-character spaces. Consequently, our proposed approach achieves superior performance on not only two public curved text detection datasets, namely Total-Text and SCUT-CTW1500, but also a multi-oriented text detection dataset, namely MSRA-TD500.