In order to solve the problem of group decision making of hesitant language type Z-numbers (HLZ-numbers)，a group decision method is proposed under the information environment of hesitant language type Z-numbers in the unknown expert attribute weight. First，two kinds of new language scale functions (LSF) and related properties are proposed on the basis of Z-number theory and language type set，and a new language scale function is used to measure language information. Secondly，the distance formula between hesitant language type Z-numbers is proposed by combining the two new language scale functions，and a new method is established based on the new language scale function. The linguistic scale function of hesitant Z-numbers group decision making model is set up. The model combines the integration operator theory and uses the interval number arithmetic average to make the decision matrix set into a comprehensive matrix，by establishing a two-dimensional possibility degree comparison possibility matrix，and then sorting by the sort vector method. Finally，an example is given to illustrate the effectiveness and feasibility of the method.