Recent vision-language understanding approaches adopt a multi-modal transformer pre-training and finetuning paradigm. Prior work learns representations of text tokens and visual features with cross-attention mechanisms and captures the alignment solely based on indirect signals. In this work, we propose to enhance the alignment mechanism by incorporating image scene graph structures as the bridge between the two modalities, and learning with new contrastive objectives. In our preliminary study on the challenging compositional visual question answering task, we show the proposed approach achieves improved results, demonstrating potentials to enhance vision-language understanding.