The identification of customer requirements (CRs) priority is the beginning of Product-service system (PSS) design, which identifies the direction of enterprise resource allocation. In order to accurately reflect customer’s intrinsic requirements in PSS design, a hierarchical model based on the means-end chain theory is constructed to capture CRs from the perspective of customer expectations in this paper, and then a method combining cloud model, fuzzy Decision-making Trial and Evaluation Laboratory (DEMATEL) with improved analytical Kano (A-Kano) model is proposed to identify importance priority. Cloud model and Relative Preference Relation of the triangular fuzzy number are applied to identify the basic importance with solving the problem of fuzziness and randomness in expert evaluation information. Considering the directional influence relationship among CRs, the fuzzy DEMATEL method is introduced to modify the basic importance. Based on the category criterion of CRs, an improved A-Kano model is constructed, and the importance index and satisfaction index based on customer satisfaction are introduced to identify the final importance. A case study is carried out to verify the scientificity and feasibility of the proposed method.