Most object detection methods focus only on the local information near the region proposal and ignore the object's global semantic relation and local spatial relation information, resulting in limited performance. To capture and explore these important relations, we propose a detection method based on a graph convolutional network (GCN). Two independent relation graph networks are used to obtain the global semantic information of the object in labels and the local spatial information in images. Semantic relation networks can implicitly acquire global knowledge, and by constructing a directed graph on the dataset, each node is represented by the word embedding of labels and then sent to the GCN to obtain high-level semantic representation. The spatial relation network encodes the relation by the positional relation module and the visual connection module, and enriches the object features through local key information from objects. The feature representation is further improved by aggregating the outputs of the two networks. Instead of directly disseminating visual features in the network, the dual-graph network explores more advanced feature information, giving the detector the ability to obtain key relations in labels and region proposals. Experiments on the PASCAL VOC and MS COCO datasets demonstrate that key relation information significantly improve the performance of detection with better ability to detect small objects and reasonable boduning box. The results on COCO dataset demonstrate our method obtains around 32.3% improvement on AP in terms of small objects.