Quality function deployment (QFD) is a useful design quality control tool in service enterprises and manufacturing enterprises. However, there are several issues in extant QFD frameworks, that is, in three aspects: description of evaluation information, weight determination of expert team members (TMs), and weight identification of customer requirements (CRs). In order to address these issues, a novel QFD framework is first proposed utilizing linguistic Z-numbers (LZNs) with integrated subjective and objective weights of TMs and CRs. The LZNs can represent uncertain information and the reliability of information in a specific way while the fuzzy numbers cannot. Moreover, the order relation analysis (G1) method and improved maximum consensus (MC) method are developed to get the subjective and objective weights of TMs, respectively. Further, the step-wise weight assessment ratio analysis (SWARA) method and statistical distance (SD) method are studied to acquire combined weights of CRs. Next, the proposed QFD framework is applied to a case of logistics service provider, which illustrates the availability and utility of the framework. Then, a sensitivity analysis is conducted to prove the reliability of the framework. Finally, two comparative analyses are performed to declare the advantages of the framework. Results indicate the proposed QFD framework is better than existing models.