Quality function deployment (QFD) is an effective product development and management tool, which has been broadly applied in various industries to develop and improve products or services. Nonetheless, when used in real situations, the traditional QFD method shows some important weaknesses, especially in describing experts’ opinions, weighting customer requirements, and ranking engineering characteristics. In this study, a new QFD approach integrating linguistic Z-numbers and evaluation based on distance from average solution (EDAS) method is proposed to determine the prioritization of engineering characteristics. Specially, linguistic Z-numbers are adopted to deal with the vague evaluation information provided by experts on the relationships among customer requirements and engineering characteristics. Then, the EDAS method is extended to estimate the final priority ratings of engineering characteristics. Additionally, stepwise weight assessment ratio analysis (SWARA) method is employed to derive the relative weights of customer requirements. Finally, a practical case of Panda shared car design is introduced and a comparison is conducted to verify the feasibility and effectiveness of the proposed QFD approach. The results show that the proposed linguistic Z-EDAS method can not only represent experts’ interrelation evaluation information flexibly, but also produce a more reasonable and reliable prioritization of engineering characteristics in QFD.