To promote the sustainable development of the energy economy and handle the intermittent problems of renewable energy power generation, compressed air energy storage (CAES) power generation has emerged. Site selection makes an important contribution to the success of CAES project and is a multi-criteria decision-making (MCDM) problem. This paper proposes a MCDM method based on probabilistic language term sets (PLTSs) and regret theory, and applies it to the site selection of CAES project. Firstly, this paper constructs an index system covering six criteria and sixteen sub-criteria. Secondly, PLTSs are used to describe the evaluation information of decision makers (DMs), which consider the hesitation of DMs and information uncertainty. And a new distance formula of PLTSs is defined. Thirdly, this paper considers the psychological characteristics of DMs by introducing regret theory, and further defines a comprehensive perceptual utility function to avoid the enlargement or reduction of the regret or rejoice value due to the ignorance of expected value of the plan itself. Fourthly, a weighting model of DMs weights is established by using the entropy weight method, and a criteria weight model is developed by minimizing distance deviation. Furthermore, a MCDM method is proposed. Finally, a case study is provided to verify the effectiveness and feasibility of our method. The results show that option A3 is the best choice. This work provides a scientific theoretical basis for the investment decision-making of CAES project.