With the aim of matching a pair of instances from two different modalities, cross modality mapping has attracted growing attention in the computer vision community. Existing methods usually formulate the mapping function as the similarity measure between the pair of instance features, which are embedded to a common space. However, we observe that the relationships among the instances within a single modality (intra relations) and those between the pair of heterogeneous instances (inter relations) are insufficiently explored in previous approaches. Motivated by this, we redefine the mapping function with relational reasoning via graph modeling, and further propose a GCN-based Relational Reasoning Network (RR-Net) in which inter and intra relations are efficiently computed to universally resolve the cross modality mapping problem. Concretely, we first construct two kinds of graph, i.e., Intra Graph and Inter Graph, to respectively model intra relations and inter relations. Then RR-Net updates all the node features and edge features in an iterative manner for learning intra and inter relations simultaneously. Last, RR-Net outputs the probabilities over the edges which link a pair of heterogeneous instances to estimate the mapping results. Extensive experiments on three example tasks, i.e., image classification, social recommendation and sound recognition, clearly demonstrate the superiority and universality of our proposed model.