Multi-hop reasoning has been widely studied in recent years to seek an effective and interpretable method for knowledge graph (KG) completion. Most previous reasoning methods are designed for dense KGs with enough paths between entities, but cannot work well on those sparse KGs that only contain sparse paths for reasoning. On the one hand, sparse KGs contain less information, which makes it difficult for the model to choose correct paths. On the other hand, the lack of evidential paths to target entities also makes the reasoning process difficult. To solve these problems, we propose a multi-hop reasoning model over sparse KGs, by applying novel dynamic anticipation and completion strategies: (1) The anticipation strategy utilizes the latent prediction of embedding-based models to make our model perform more potential path search over sparse KGs. (2) Based on the anticipation information, the completion strategy dynamically adds edges as additional actions during the path search, which further alleviates the sparseness problem of KGs. The experimental results on five datasets sampled from Freebase, NELL and Wikidata show that our method outperforms state-of-the-art baselines. Our codes and datasets can be obtained from https://github.com/THU-KEG/DacKGR.