Aiming at the situation that the weights of decision makers and criteria are both unknown in group decision making progress, we propose a liner method of multi-attribute decision making based on 2-dimension 2-tuple linguistic representation model. Considering the relative importance of the first dimensional information and the second dimensional information of 2-dimension 2-tuple linguistic information, the score function and distance measures, which can reflect the impact of the change of the proportion of the relative importance on the score function for comparing two 2-dimension 2-tuple linguistic information and distance measures between them, are proposed. Then, decision makers' weight and criteria weight are solved simultaneously by constructing a model that the objective function is set up based on the score function and distance measures, and constraint conditions are established based on the entropy value of decision makers. Furthermore, the corresponding weights information which makes each alternative optimal is obtained by solving different models, then the optimal alternative and rank alternatives are chosen according to the value of the objective function. Finally, the case analysis and comparison verify the effectiveness and scientificalness of the proposed method.