Within the multiple attributes group decision making problems, for the case that each decision maker has amultiplicative preference relation referring to alternatives for each attribute, a multiple attributes group decision making method of group consistency deviation entropy model based on multiplicative preference relations is proposed, in which the decision makers are assigned with different weights in each attribute, and an iteration operation is introduced to reach the group consistency. After that, the decision makers’ weighting vector can be obtained. Furthermore, with the use of deviation entropy model, the attribute weighting vector can be worked out. Then the composite multiplicative preference relation with group consistency can be generated on the basis of above two weighting vectors. Finally, a numerical example is given to illustrate the effectiveness of the proposed method.