The analytic hierarchy process (AHP) is widely used as a multi-criteria decision-making method in practical applications. Several researchers have expanded the AHP method to D numbers AHP (D-AHP) to apply AHP to an uncertain decision-making environment. D numbers is an extension of the Dempster–Shafer (D–S) theory, which overcomes the shortcomings of the D–S theory and can effectively express uncertain information. With the deepening of research on the AHP method, the best–worst method (BWM) was proposed as an improvement to the AHP method. The BWM can lower the inconsistency in results and reduce the number of required pairwise comparisons. Although some researchers have extended the BWM method to an uncertain environment and proposed fuzzy BWM methods, these methods cannot handle some special situations, such as when the subjective evaluations of experts are conflicting or altogether missing. To apply the BWM method to these special situations, this study suggests combining the BWM with D numbers and proposes D numbers BWM (D-BWM) weighting model. First of all, we discuss D numbers extended fuzzy preference relations (DNFPRs). Afterwards, we design an algorithm to select the best and worst criteria based on the DNFPRs by calculating the out-degrees and in-degrees. Furthermore, we develop a linear programming model to derive the weights of criteria, and then propose a consistency ratio to check the reliability of the derived results. The experimental results show that the D-BWM method is more suitable for realistic decision-making because of its simplicity and sensitivity to subjective information. Finally, the proposed method is applied to evaluate the environmental performances of 30 provincial administrative regions of China.