For multi-criteria group decision-making problem, in which the attribute weights are unknown, and the attribute value of alternatives is in the form of intuitionistic linguistic number, a group decision making method based on intuitionistic linguistic entropy and generalized intuitionistic linguistic operators is proposed. First, the intuitionistic linguistic entropy is defined and used to determine the attribute weights. Then three generalized intuitionistic linguistic operators are introduced,including the generalized intuitionistic linguistic weighted geometric averaging (GILWGA) operator, the generalized intuitionistic linguistic ordered weighted geometric (GILOWG) operator and the generalized intuitionistic linguistic hybrid geometric (GILHG) operators, and the GILWGA and GILHG operator are used to aggregate information. Furthermore, using the score function and accuracy function based on the intuitionistic linguistic numbers to sort the alternatives and obtain the best alternative. Finally, an illustrative example is given to demonstrate the feasibility and validity of the developed method.