Image captioning which automatically generates natural language descriptions for images has attracted lots of research attentions and there have been substantial progresses with attention based captioning methods. However, most attention-based image captioning methods focus on extracting visual information in regions of interest for sentence generation and usually ignore the relational reasoning among those regions of interest in an image. Moreover, these methods do not take into account previously attended regions which can be used to guide the subsequent attention selection. In this paper, we propose a novel method to implicitly model the relationship among regions of interest in an image with a graph neural network, as well as a novel context-aware attention mechanism to guide attention selection by fully memorizing previously attended visual content. Compared with the existing attention-based image captioning methods, ours can not only learn relation-aware visual representations for image captioning, but also consider historical context information on previous attention. We perform extensive experiments on two public benchmark datasets: MS COCO and Flickr30K, and the experimental results indicate that our proposed method is able to outperform various state-of-the-art methods in terms of the widely used evaluation metrics.