Temporal knowledge graphs (TKGs), consisting of graph snapshots evolving over time, have attracted substantial research attention in various areas like recommender systems and relation networks. Although significant research efforts have been devoted to this field, the regularity and abruptness of graph evolution make it still challenging to model temporal dynamics in TKGs. Existing works only characterize the short-term evolution due to the limitations of modeling long sequences, or lack consideration of fine-grained differences between recent snapshots in time. To tackle the issues, we propose LSEN (Long Short-Term Evolution Learning Network), an effective model that jointly captures short-term and long-term evolution patterns in TKGs. By introducing a short-term and a long-term evolution pattern mining module, we boost the memorization and generalization of LSEN for TKG reasoning. Specifically, the short-term module of LSEN simultaneously consider the topology structure at each moment and model the chronologically sequential effect across recent snapshots. In addition, we devise a long-term module leveraging the frequencies of constrained triple occurrences to explore long-term evolution patterns in the entire historical sequence. We conduct extensive experiments on five real-world datasets, and LSEN achieves state-of-the-art results, demonstrating the significant superiority of our method.