Large language models achieve state-of-the-art performance on sequence generation evaluation, but typically have a large number of parameters. This is a computational challenge as presented by applying their evaluation capability at scale. To overcome the challenge, in this paper, we propose ECT, an evaluation capability transfer method, to transfer the evaluation capability from LLMs to relatively lightweight language models. Based on the proposed ECT, we learn various evaluation models from ChatGPT, and employ them as reward models to improve sequence generation models via reinforcement learning and reranking approaches. Experimental results on machine translation, text style transfer, and summarization tasks demonstrate the effectiveness of our ECT. Notably, applying the learned evaluation models to sequence generation models results in better generated sequences as evaluated by commonly used metrics and ChatGPT.