Reliability of information can directly affect the accuracy of decision-making. Compared with classical fuzzy sets, Z-number takes into account the uncertainty in information generation process and reliability of information. Z-number can also be an intuitive and effective description form of decision information. Existing research on the distance measure of Z-number is rare, and most of the research works cannot reflect well the advantages of Z-information and the characteristics of Z-number. Given this research gap, this paper simultaneously considered the randomness and fuzziness of Z-number and defined the comprehensive weighted distance measure of Z-number. To extend classic VlseKriterijum-ska Optimizacija I Kompromisno Resenje (VIKOR) method to the Z-information environment, we suggested the Z-VIKOR method based on the proposed distance measure. This method is convenient and effective for the direct computation of Z-numbers. We also provided an example of multicriteria decision-making for selecting regional circular economy development plan to illustrate the feasibility and validity of our proposed method. We then verified the applicability and superiority of our method through comparative analyses with other existing methods.