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A new method is proposed to solve multiple attribute group decision making problems with linguistic assessment information. In the method, the two-tuple linguistic representation developed in recent years is used to aggregate the linguistic assessment information. According to the traditional ideas of grey relational analysis, the optimal alternative(s) is determined by calculating the linguistic degree of grey relation of every alternative and two-tuple linguistic positive ideal solution and two-tuple linguistic negative ideal solution. It is based on the concept that the optimal alternative should have the largest degree of grey relation from positive ideal solution and the smallest degree of grey relation from the negative ideal solution. The method has exact characteristic in linguistic information processing. It avoided information distortion and losing which occur formerly in the linguistic information processing. Finally, a numerical example is used to illustrate the use of the proposed method. The result shows the approach is simple, effective and easy to calculate.