A linguistic group decision-making problem with the judgement reliability of decision makers is studied. To the problem on the reliability of self-selection which is expressed in terms of linguistic variables, a method to measure reliability based on the linguistic information degree of greyness is constructed. According to the indicators of group consensus, the linguistic information degree of greyness and prior subjective information, a method to calculate comprehensive weights of experts is proposed. On the basis of the linguistic information degree of greyness of information aggregation, the method of measuring and analyzing the reliability of decision-making is established. Then the sorting algorithm considering the linguistic information degree of greyness is proposed as well. A numerical example is given to illustrate the effectiveness of the proposed method.