Link prediction is a fundamental task in dynamic graph learning (DGL), inherently shaped by the topology of the DG. Recent advancements in dynamic graph neural networks (DGNN), primarily by modeling the relationships among nodes via a message passing scheme, have significantly improved link prediction performance. However, DGNNs heavily rely on the pairwise node interactions, which neglect the common neighbor interaction in DGL. To address this limitation, we propose a High-order Graph Neural Networks with Common Neighbor Awareness (HGNN-CNA) for link prediction with two-fold ideas: a) estimating correlation score by considering multi-hop common neighbors for capturing the complex interaction between nodes; b) fusing the correlation into the message-passing process to consider common neighbor interaction directly in DGL. Experimental results on three real DGs demonstrate that the proposed HGNN-CNA acquires a significant accuracy gain over several state-of-the-art models on the link prediction task.