For the multi-criterion group decision-making problems with normal clouds under the criterion set, a decision-making method based on cosine close degrees and group consensus degrees is proposed. In the method, firstly, the normal cloud decision-making matrices of the experts are transformed into general normal stochastic decision-making matrices. Then, by using the linear combination method of normal clouds, the linear weighted general normal stochastic variables of the alternatives are derived. Furthermore, based on ideal alternatives, the cosine similarity degrees, cosine close degrees and ranking results are attained by each expert. After that, through the group consensus degree, the consistency degree of the decision-making opinions of the expert sets is worked out. Accordingly, the weighted cosine similarity degree, weighted cosine close degree and the comprehensive ranking order are gained. Finally, the feasibility and effectiveness of the proposed method are verified by the comparative analysis of an illustrative example.