Dynamic link prediction is essential for a wide range of domains, including social networks, bioinformatics, knowledge bases, and recommender systems. Existing works have demonstrated that structural information and temporal information are two of the most important information for this problem. However, existing works either focus on modeling them independently or modeling the temporal dynamics of a single structural scale, neglecting the complex correlations among them. This paper proposes to model the inherent correlations among the evolving dynamics of different structural scales for dynamic link prediction. Following this idea, we propose an Attentional Multi-scale Co-evolving Network (AMCNet). Specifically, We model multi-scale structural information by a motif-based graph neural network with multi-scale pooling. Then, we design a hierarchical attention-based sequence-to-sequence model for learning the complex correlations among the evolution dynamics of different structural scales. Extensive experiments on four real-world datasets with different characteristics demonstrate that AMCNet significantly outperforms the state-of-the-art in both single-step and multi-step dynamic link prediction tasks.