Zero-shot relational triplet extraction is a vital solution to the problem of fact extracted from unstructured text without labeled training data. In the task, the data is divided into seen and unseen relations for training and prediction, respectively. A strategy that trains a generative model based on seen data first and generates training samples for unseen data has been shown to be effective in solving this task. However, this strategy is severely limited by error propagation caused by generated noisy data. To address this issue, prompts may provide a feasible route since they have been widely utilized in cross-domain tasks. In this paper, three preliminary experiments reveal the effectiveness of prompts for the task of triplet extraction and its internal mechanism. Specifically, the method using prompts can control the domain.11The term is quite loosely used in NLP. In this paper, domain is used to represent which relations may be associated with the given sentence. For more detailed information, please refer to Appendix A. Further, we propose a simple but effective model for zero-shot relational triplet extraction, which leverages zero-shot text classification to first determine the prompts of unseen relations aiming to optimize both its domain and length, and then extracts triplets via prompt-driven strategy. Extensive experiments are conducted on two public datasets, demonstrating that the proposed model achieves a better performance than baselines.