Serving as an effective tool for describing both randomness and fuzziness of qualitative concepts, the cloud model has become a common topic of research. By realizing the uncertain transformation between qualitative concepts and quantitative data, the cloud model provides a new way to deal with group decision making problems in the linguistic environment. However, classical methods based on the cloud model mainly focus on addressing problems with a small number of decision makers. In this paper, we apply the cloud model to the decision making problems which involve a large group of decision makers. Specifically, we first define a new measure of fuzzy distance for clouds based on the α-cuts. On the basis of the proposed fuzzy distance measure, we then present a new similarity measure between clouds. Next, we construct an improved clustering approach based on the traditional hierarchical clustering algorithm. Furthermore, we develop a hybrid weight scheme to obtain the cluster weights, which takes both the subgroup size and the variance into consideration. Moreover, we present a consensus-based method based on the cloud model for large group decision making (LGDM) with linguistic information. Finally, in order to confirm the validity and effectiveness of the proposed method, we give an application in the context of the Belt and Road Initiative of China, and perform some detailed comparisons to show the advantages of the proposed method.