Abstract：The evaluations of the alternatives can be normal clouds under the criterion set. As for such multi-criterion group decision-making problems, a decision-making method based on cosine close degrees and group consensus degrees is proposed. In the method, firstly, according to the relation between normal clouds and normal stochastic variables, the normal cloud decision-making matrices are transformed into general normal stochastic decision-making matrices. Then, using the linear combination method of normal clouds, the linear weighted general normal stochastic variables of the alternatives are gotten by each expert. 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. If the consistency degree is less than or equal to 0.5, the initial decision information may be adjusted. Accordingly, the weighted cosine similarity degree, weighted cosine close degree and the comprehensive ranking order are gained. Finally, the validity and feasibility of the method are verified by the comparative analysis of an illustrative example.