Temporal knowledge graph forecasting aims to reason over known facts to complete the missing links in the future. Existing methods are highly dependent on the structures of temporal knowledge graphs and commonly utilize recurrent or graph neural networks for forecasting. However, entities that are infrequently observed or have not been seen recently face challenges in learning effective knowledge representations due to insufficient structural contexts. To address the above disadvantages, in this paper, we propose a Contrastive Prompt-based framework with Entity background information for TKG forecasting, which we named CoPET. Specifically, to bring the time-invariant entity background information to time-variant structural information, we employ a dual encoder architecture consisting of a candidate encoder and a query encoder. A contrastive learning framework is used to encourage the query representation to be closer to the candidate representation. We further propose three kinds of trainable time-variant prompts aimed at capturing temporal structural information. Experiments on two datasets demonstrate that our method is effective and stays competitive in inference with limited structural information. Our code is available at https://github.com/qianxinying/CoPET.