The approach of linguistic multi-attribute group decision making based on generalized precedence ordering method is proposed for dealing with the multiple attributes group decision making problems with linguistic assessment information. In this method, linguistic assessment information is transformed into generalized precedence ordering numbers in the form of 2-tuple linguistic by means of expanding effectively the classic precedence ordering method and applying the concept of 2-tuple linguistic with latest development in recent years. On this basis, the attribute weight is solved based on the idea of the deviation of generalized precedence ordering numbers, and then the optimal alternative is determined. The proposed approach processes the linguistic information exactly, avoids the loss and distortion of information effectively. Finally, the analysis result of the case of risk investment shows the conciseness and effectiveness of the proposed method.