Temporal Knowledge Graphs (TKG) reasoning has emerged as a powerful methodology for prediction in various domains. Unlike traditional Knowledge Graphs(KG), TKGs introduce a critical time dimension to the graph structure. Existing TKG reasoning methods expose two important limitations. The first is they are primarily designed to predict the immediate next time step. When applied to multi-step predictions, this leads to an iterative process that compromises prediction efficiency. The second limitation is their performance often depends on short-term memory and overlook long-term global information. To overcome these limitations, we introduce the Echo State Temporal Knowledge Graph Network (ESTN), an innovative approach leveraging the Echo State Networks (ESN) for TKG reasoning. Specifically, the ESTN contains a Graph Embedder (GE) which integrates both short-term and long-term information within the TKG, enhancing the depth and accuracy of the data representation in graph latent space (embeddings). A Time Module (TM) is designed to facilitate direct prediction over multiple time steps, significantly improved the prediction efficiency. Extensive experiments demonstrate that our method not only show robust performance, but also offers an alternative approach to TKG reasoning, emphasizing how the distinct features of ESN can be effectively harnessed in TKG reasoning tasks.