A new method is proposed for multiple attribute group decision making problems with multigranularity interval linguistic information based on interval twotuple linguistic information and maximizing deviation. Firstly, a transformation function is given to uniform the multigranularity interval linguistic preference information into the form of interval twotuple linguistic information in basic linguistic term set. Then, an objective programming model based on maximizing deviation, by which the attribute weight information is completely unknown, is established. By solving this model, a simple and exact formula can be used to determine the attribute weights. The interval twotuple aggregation operator is utilized to aggregate the linguistic assessment information corresponding to each alternative. The possibility degree of interval twotuple linguistic information is utilized to the result of aggregation in order to rank the alternatives and select the most desirable one(s). Finally, an example is given to demonstrate the feasibility and efficiency of the proposed method.