In order to solve the problem of utility of Z-number, a method of calculating the utility of discrete Z-number is proposed. Firstly, according to the two distribution patterns of membership value of the discrete Z-number, the two different methods of transforming discrete fuzzy number into Gauss fuzzy number and triangular fuzzy number are proposed based on 3σ principle and linear function respectively, so that the discrete Z-number is transformed into continuous Z-number. Then based on the utility function of continuous Z-number and the four situations of Z-number after being transformed, the calculation method of utility of the discrete Z-number is proposed. Finally, through a multi-attribute decision-making case, the proposed transforming methods and calculation method are used to transform objective attribute information into utility value, via multiple attribute decision-making method based on information entropy, the optimal sorting of decision-making objective is given, so that the effectiveness and feasibility of transforming method for the two discrete fuzzy numbers and calculation method of the utility of the discrete Z-number are verified.