To deal with the hybrid multi-attribute decision-making problem with attribute weight information unknown, a grey relation analysis method based on two-tuple linguistic consistency is proposed. Firstly, aiming at the problem of heterogeneous decision information, an unifier method is proposed to switch all the decision information to 2-tuple linguistic information. Then, according to the maximizing deviation, the index weight can be objectively determined, and the optimal alternative is determined by calculating the linguistic degree of grey relation of every alternative and ideal solution. Finally, a numerical example of the performance evaluation of the suppliers in one supply chains is given to carry on the confirmation to the practicable method which can provide more valuable information on decision-making.