The concept of the generalized intuitionistic fuzzy entropy is developed by considering the intuitive and fuzzy information with respect to an intuitionistic fuzzy set(IFS).The influence of an IFS's respective information on its generalized intuitionistic fuzzy entropy is analyzed.With the premise of determining the parameters of the generalized intuitionistic fuzzy entropy reasonably, an efficient method based on the entropy weight approach is proposed to determine the weights of decision makers and that of attributes simultaneously.The proposed weight determination method can be applied to address the multi-attribute group decision making problem in which the weight information is completely unknown.Finally, a numerical example is provided to illustrate the effectiveness and feasibility of the proposed method.